多角数のソースを表示

'''多角数'''（たかくすう、{{lang-en-short|polygonal number}}）とは、[[正多角形]]の形に点を並べたときにそこに含まれる点の総数にあたる[[自然数]]である。'''多角形数'''ともいう。

== 例 ==
例えば、10 個の点は
:{|
| align="center" | [[Image:GrayDotX.svg|16px|*]]<br />[[Image:GrayDotX.svg|16px|*]][[Image:GrayDotX.svg|16px|*]]<br />[[Image:GrayDotX.svg|16px|*]][[Image:GrayDotX.svg|16px|*]][[Image:GrayDotX.svg|16px|*]]<br />[[Image:GrayDotX.svg|16px|*]][[Image:GrayDotX.svg|16px|*]][[Image:GrayDotX.svg|16px|*]][[Image:GrayDotX.svg|16px|*]]
|}
このように[[正三角形]]の形に並べることができるので 10 は[[三角数]]である。また、16 個の点は
:{|
| align="center" | [[Image:GrayDot.svg|16px|*]][[Image:GrayDot.svg|16px|*]][[Image:GrayDot.svg|16px|*]][[Image:GrayDot.svg|16px|*]]<br />[[Image:GrayDot.svg|16px|*]][[Image:GrayDot.svg|16px|*]][[Image:GrayDot.svg|16px|*]][[Image:GrayDot.svg|16px|*]]<br />[[Image:GrayDot.svg|16px|*]][[Image:GrayDot.svg|16px|*]][[Image:GrayDot.svg|16px|*]][[Image:GrayDot.svg|16px|*]]<br />[[Image:GrayDot.svg|16px|*]][[Image:GrayDot.svg|16px|*]][[Image:GrayDot.svg|16px|*]][[Image:GrayDot.svg|16px|*]]
|}
このように[[正方形]]の形に並べることができ、16 は四角数（[[平方数]]）である。

三角数、四角数、[[六角数]]の例を以下に示す。

;三角数
:{|
! 1 !! !! 3 !! !! 6 !! !! 10
|- align="center" valign="top"
|[[Image:RedDotX.svg|16px|*]]
|
|[[Image:GrayDotX.svg|16px|*]]<br />[[Image:RedDotX.svg|16px|*]][[Image:RedDotX.svg|16px|*]]
|
|[[Image:GrayDotX.svg|16px|*]]<br />[[Image:GrayDotX.svg|16px|*]][[Image:GrayDotX.svg|16px|*]]<br />[[Image:RedDotX.svg|16px|*]][[Image:RedDotX.svg|16px|*]][[Image:RedDotX.svg|16px|*]]
|
|[[Image:GrayDotX.svg|16px|*]]<br />[[Image:GrayDotX.svg|16px|*]][[Image:GrayDotX.svg|16px|*]]<br />[[Image:GrayDotX.svg|16px|*]][[Image:GrayDotX.svg|16px|*]][[Image:GrayDotX.svg|16px|*]]<br />[[Image:RedDotX.svg|16px|*]][[Image:RedDotX.svg|16px|*]][[Image:RedDotX.svg|16px|*]][[Image:RedDotX.svg|16px|*]]
|}

;四角数
:{|
! 1 !! !! 4 !! !! 9 !! !! 16
|- align="center" valign="top"
|[[Image:RedDot.svg|16px|*]]
|
|[[Image:GrayDot.svg|16px|*]][[Image:RedDot.svg|16px|*]]<br />[[Image:RedDot.svg|16px|*]][[Image:RedDot.svg|16px|*]]
|
|[[Image:GrayDot.svg|16px|*]][[Image:GrayDot.svg|16px|*]][[Image:RedDot.svg|16px|*]]<br />[[Image:GrayDot.svg|16px|*]][[Image:GrayDot.svg|16px|*]][[Image:RedDot.svg|16px|*]]<br />[[Image:RedDot.svg|16px|*]][[Image:RedDot.svg|16px|*]][[Image:RedDot.svg|16px|*]]
|
|[[Image:GrayDot.svg|16px|*]][[Image:GrayDot.svg|16px|*]][[Image:GrayDot.svg|16px|*]][[Image:RedDot.svg|16px|*]]<br />[[Image:GrayDot.svg|16px|*]][[Image:GrayDot.svg|16px|*]][[Image:GrayDot.svg|16px|*]][[Image:RedDot.svg|16px|*]]<br />[[Image:GrayDot.svg|16px|*]][[Image:GrayDot.svg|16px|*]][[Image:GrayDot.svg|16px|*]][[Image:RedDot.svg|16px|*]]<br />[[Image:RedDot.svg|16px|*]][[Image:RedDot.svg|16px|*]][[Image:RedDot.svg|16px|*]][[Image:RedDot.svg|16px|*]]
|}

;六角数
:{|
! 1 !! !! 6 !! !! 15 !! !! 28
|- align="center" valign="middle"
|[[Image:RedDotX.svg|16px|*]]
|
|[[Image:RedDot.svg|16px|*]][[Image:RedDotX.svg|16px|*]]<br />[[Image:GrayDotX.svg|16px|*]][[Image:Blank300.png|15px|&nbsp;]][[Image:RedDotX.svg|16px|*]]<br />[[Image:RedDotX.svg|16px|*]][[Image:RedDotX.svg|16px|*]]
|
|[[Image:RedDot.svg|16px|*]][[Image:RedDotX.svg|16px|*]][[Image:RedDotX.svg|16px|*]]<br />[[Image:GrayDotX.svg|16px|*]][[Image:GrayDotX.svg|16px|*]][[Image:Blank300.png|15px|&nbsp;]][[Image:RedDotX.svg|16px|*]]<br />[[Image:GrayDotX.svg|16px|*]][[Image:Blank300.png|15px|&nbsp;]][[Image:GrayDotX.svg|16px|*]][[Image:Blank300.png|15px|&nbsp;]][[Image:RedDotX.svg|16px|*]]<br />[[Image:GrayDotX.svg|16px|*]][[Image:GrayDotX.svg|16px|*]][[Image:Blank300.png|15px|&nbsp;]][[Image:RedDotX.svg|16px|*]]<br />[[Image:RedDot.svg|16px|*]][[Image:RedDotX.svg|16px|*]][[Image:RedDotX.svg|16px|*]]
|
|[[Image:RedDot.svg|16px|*]][[Image:RedDot.svg|16px|*]][[Image:RedDotX.svg|16px|*]][[Image:RedDotX.svg|16px|*]]<br />[[Image:GrayDotX.svg|16px|*]][[Image:GrayDotX.svg|16px|*]][[Image:GrayDotX.svg|16px|*]][[Image:Blank300.png|15px|&nbsp;]][[Image:RedDotX.svg|16px|*]]<br />[[Image:GrayDotX.svg|16px|*]][[Image:GrayDotX.svg|16px|*]][[Image:Blank300.png|15px|&nbsp;]][[Image:GrayDotX.svg|16px|*]][[Image:Blank300.png|15px|&nbsp;]][[Image:RedDotX.svg|16px|*]]<br />[[Image:GrayDotX.svg|16px|*]][[Image:Blank300.png|15px|&nbsp;]][[Image:GrayDotX.svg|16px|*]][[Image:Blank300.png|15px|&nbsp;]][[Image:GrayDotX.svg|16px|*]][[Image:Blank300.png|15px|&nbsp;]][[Image:RedDotX.svg|16px|*]]<br />[[Image:GrayDotX.svg|16px|*]][[Image:GrayDotX.svg|16px|*]][[Image:Blank300.png|15px|&nbsp;]][[Image:GrayDotX.svg|16px|*]][[Image:Blank300.png|15px|&nbsp;]][[Image:RedDotX.svg|16px|*]]<br />[[Image:GrayDotX.svg|16px|*]][[Image:GrayDotX.svg|16px|*]][[Image:GrayDotX.svg|16px|*]][[Image:Blank300.png|15px|&nbsp;]][[Image:RedDotX.svg|16px|*]]<br />[[Image:RedDot.svg|16px|*]][[Image:RedDot.svg|16px|*]][[Image:RedDotX.svg|16px|*]][[Image:RedDotX.svg|16px|*]]
|}

[[五角数]]以上では、点を[[回転対称]]には並べないことに注意。

== 一般化 ==
0 番目の多角数は全て、形式的に 0 とみなすことができる。

''n'' 番目の ''p'' 角数を ''P''<sub>''p'',''n''</sub> とすると上の図から
: <math>P_{p,n+1} - P_{p,n} = (p-2)n + 1\,</math>
となり、したがって ''P''<sub>''p'',''n''</sub> は[[等差数列]]の和
: <math>\begin{align} P_{p,n} &= \sum_{k=0}^{n-1} \left\{ (p-2)k+1 \right\}
\\ &= \frac{1}{2} n \left[1 + \left\{ (p-2)(n-1) + 1 \right\} \right]
\\ &= \frac{(p-2)n^2 - (p-4)n}{2}
\end{align}</math>
となる。

この式から、2 番目の ''p'' 角数は ''p'' であり、3 番目の ''p'' 角数は 3(''p'' &minus; 1) であることなどが分かる。

なおここで、形式的に「二角数」(''p'' = 2) を考えると、
: <math>P_{2,n} = n \,</math>
となり、自然数列そのものになる。これは、点を[[直線]]状に並べることに相当する。ただし[[古代ギリシャ]]の数学者が直線数と呼んでいたのは、[[長方形|矩形]]に並べられることができないことからである。

== 性質 ==
* 任意の自然数は、[[高々_(数学)|高々]] ''p'' 個の ''p'' 角数の和で表せる。これを[[多角数定理]]という。
* 1 番目の多角数は 1、2 番目の ''p'' 角数は ''p'' である。したがって、2 以外の自然数はなんらかの多角数である。
* 3 番目以降の多角数は、[[合成数]]である。
* ''n'' 番目の ''p'' 角数は、''n'' が[[偶数]]で ''p'' が[[奇数]]のときに限り、''n'' の[[倍数]]でない。
* ''n'' 番目の ''p'' 角数と ''n'' + 1 番目の ''p'' 角数の差は、(''p'' − 2) ''n'' + 1 である。
* ''n'' 番目の ''p'' 角数と ''n'' 番目の ''p'' + 1 角数の差は、''p'' によらず ''n'' だけで決まり、''n'' − 1 番目の三角数に等しい。（次の表を縦に読むと等差数列になっている。）

== 数表 ==
{| class="wikitable"  style="text-align:right"
|+ オンライン整数列大辞典に掲載されている多角数（三十角数まで）
|-
! 名前 !! 一般式 !! ''n'' = 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9 !! 10 !! 11 !! 12 !! 13 !! [[オンライン整数列大辞典]] !! リスト
|-
|-
| <center>[[三角数]]</center> || style="text-align:left" |(''n''<sup>2</sup> + ''n'')/2 || <center>[[1]]</center> || <center>[[3]]</center> || <center>[[6]]</center> || <center>[[10]]</center> || <center>[[15]]</center> || <center>[[21]]</center> || <center>[[28]]</center> || <center>[[36]]</center> || <center>[[45]]</center> || <center>[[55]]</center> || <center>[[66]]</center> || <center>[[78]]</center> || <center>[[91]]</center> || {{OEIS2C|A000217}} || [https://oeis.org/A000217/b000217.txt Table of n. a(n) for n = 0..]
|-
| <center>[[平方数|四角数]]</center> ||style="text-align:left" | ''n''<sup>2</sup> || <center>[[1]]</center> || <center>[[4]]</center> || <center>[[9]]</center> || <center>[[16]]</center> || <center>[[25]]</center> || <center>[[36]]</center> || <center>[[49]]</center> || <center>[[64]]</center> || <center>[[81]]</center> || <center>[[100]]</center> || <center>[[121]]</center> || <center>[[144]]</center> || <center>[[169]]</center> || {{OEIS2C|A000290}} || [https://oeis.org/A000290/b000290.txt  Table of n, a(n) for n = 0..]
|-
| <center>[[五角数]]</center> ||style="text-align:left" | (3''n''<sup>2</sup> − ''n'')/2 || <center>[[1]]</center> || <center>[[5]]</center> || <center>[[12]]</center> || <center>[[22]]</center> || <center>[[35]]</center> || <center>[[51]]</center> || <center>[[70]]</center> || <center>[[92]]</center> || <center>[[117]]</center> || <center>[[145]]</center> || <center>[[176]]</center> || <center>[[210]]</center> || <center>[[247]]</center> || {{OEIS2C|A000326}} || [https://oeis.org/A000326/b000326.txt  Table of n, a(n) for n = 0..]

|-
| <center>[[六角数]]</center> ||style="text-align:left" | 2''n''<sup>2</sup> − ''n'' || <center>[[1]]</center> || <center>[[6]]</center> || <center>[[15]]</center> || <center>[[28]]</center> || <center>[[45]]</center> || <center>[[66]]</center> || <center>[[91]]</center> || <center>[[120]]</center> || <center>[[153]]</center> || <center>[[190]]</center> || <center>[[231]]</center> || <center>[[276]]</center> || <center>[[325]]</center> || {{OEIS2C|A000384}} || [https://oeis.org/A000384/b000384.txt  Table of n, a(n) for n = 0..]

|-
| <center>[[七角数]]</center> || style="text-align:left" |(5''n''<sup>2</sup> − 3''n'')/2 || <center>[[1]]</center> || <center>[[7]]</center> || [[18]] || <center>[[34]]</center> || <center>[[55]]</center> || <center>[[81]]</center> || [[112]] || [[148]] || <center>[[189]]</center> || <center>[[235]]</center> || <center>[[286]]</center> || <center>[[342]]</center> || <center>[[403]]</center> || {{OEIS2C|A000566}} || [https://oeis.org/A000566/b000566.txt  Table of n, a(n) for n = 0..]

|-
| <center>[[八角数]]</center> ||style="text-align:left" | 3''n''<sup>2</sup> − 2''n'' || <center>[[1]]</center> || <center>[[8]]</center> || [[21]] || <center>[[40]]</center> || <center>[[65]]</center> || <center>[[96]]</center> || [[133]] || [[176]] || <center>[[225]]</center> || <center>[[280]]</center> || <center>[[341]]</center> || <center>[[408]]</center> || <center>[[481]]</center> || {{OEIS2C|A000567}} || [https://oeis.org/A000567/b000567.txt  Table of n, a(n) for n = 0..]

|-
| <center>[[九角数]]</center> || style="text-align:left" |(7''n''<sup>2</sup> − 5''n'')/2 || <center>[[1]]</center> || <center>[[9]]</center> || [[24]] || <center>[[46]]</center> || <center>[[75]]</center> || [[111]] || [[154]] || [[204]] || <center>[[261]]</center> || <center>[[325]]</center> || <center>[[396]]</center> || <center>[[474]]</center> || <center>[[559]]</center> || {{OEIS2C|A001106}} || [https://oeis.org/A001106/b001106.txt  Table of n, a(n) for n = 0..]

|-
| <center>[[十角数]]</center> || style="text-align:left" |4''n''<sup>2</sup> − 3''n'' || <center>[[1]]</center> || [[10]] || [[27]] || <center>[[52]]</center> || <center>[[85]]</center> || [[126]] || [[175]] || [[232]] || <center>[[297]]</center> || <center>[[370]]</center> || <center>[[451]]</center> || <center>[[540]]</center> || <center>[[637]]</center> || {{OEIS2C|A001107}} || [https://oeis.org/A001107/b001107.txt  Table of n, a(n) for n = 0..]

|-
| <center>十一角数</center> ||style="text-align:left" | (9''n''<sup>2</sup> − 7''n'')/2 || <center>[[1]]</center> || [[11]] || [[30]] || <center>[[58]]</center> || <center>[[95]]</center> || [[141]] || [[196]] || [[260]] || <center>[[333]]</center> || <center>[[415]]</center> || <center>[[506]]</center> || <center>[[606]]</center> || <center>[[715]]</center> || {{OEIS2C|A051682}} || [https://oeis.org/A051682/b051682.txt  Table of n, a(n) for n = 0..]

|-
| <center>[[十二角数]]</center> ||style="text-align:left" | 5''n''<sup>2</sup> − 4''n'' || <center>[[1]]</center> || [[12]] || [[33]] || <center>[[64]]</center> || [[105]] || [[156]] || [[217]] || [[288]] || <center>[[369]]</center> || <center>[[460]]</center> || <center>[[561]]</center> || <center>[[672]]</center> || <center>793</center> || {{OEIS2C|A051624}} || [https://oeis.org/A051624/b051624.txt  Table of n, a(n) for n = 0..]

|-
| <center>十三角数</center> ||style="text-align:left" | (11''n''<sup>2</sup> − 9''n'')/2 || <center>[[1]]</center> || [[13]] || [[36]] || <center>[[70]]</center> || [[115]] || [[171]] || [[238]] || [[316]] || <center>[[405]]</center> || <center>[[505]]</center> || <center>[[616]]</center> || <center>[[738]]</center> || <center>[[871]]</center> || {{OEIS2C|A051865}} || [https://oeis.org/A051865/b051865.txt  Table of n, a(n) for n = 0..]

|-
| <center>十四角数</center> ||style="text-align:left" | 6''n''<sup>2</sup> − 5''n'' || <center>[[1]]</center> || [[14]] || [[39]] || <center>[[76]]</center> || [[125]] || [[186]] || [[259]] || [[344]] || <center>[[441]]</center> || <center>[[550]]</center> || <center>[[671]]</center> || <center>804</center> || <center>949</center> || {{OEIS2C|A051866}} || [https://oeis.org/A051866/b051866.txt  Table of n, a(n) for n = 0..]

|-
| <center>十五角数</center> ||style="text-align:left" | (13''n''<sup>2</sup> − 11''n'')/2 || <center>[[1]]</center> || [[15]] || [[42]] || <center>[[82]]</center> || [[135]] || [[201]] || [[280]] || [[372]] || <center>[[477]]</center> || <center>[[595]]</center> || <center>726</center> || <center>870</center> || 1027 || {{OEIS2C|A051867}} || [https://oeis.org/A051867/b051867.txt  Table of n, a(n) for n = 0..]

|-
| <center>十六角数</center> ||style="text-align:left" | 7''n''<sup>2</sup> − 6''n'' || <center>[[1]]</center> || [[16]] || [[45]] || <center>[[88]]</center> || [[145]] || [[216]] || [[301]] || [[400]] || <center>[[513]]</center> || <center>[[640]]</center> || <center>[[781]]</center> || <center>936</center> || 1105 || {{OEIS2C|A051868}} || [https://oeis.org/A051868/b051868.txt  Table of n, a(n) for n = 0..]

|-
| <center>十七角数</center> ||style="text-align:left" | (15''n''<sup>2</sup> − 13''n'')/2 || <center>[[1]]</center> || [[17]] || [[48]] || <center>[[94]]</center> || [[155]] || [[231]] || [[322]] || [[428]] || <center>[[549]]</center> || <center>[[685]]</center> || <center>[[836]]</center> || [[1002]] || 1183 || {{OEIS2C|A051869}} || [https://oeis.org/A051869/b051869.txt  Table of n, a(n) for n = 0..]

|-
| <center>十八角数</center> ||style="text-align:left" | 8''n''<sup>2</sup> − 7''n'' || <center>[[1]]</center> || [[18]] || [[51]] || [[100]] || [[165]] || [[246]] || [[343]] || [[456]] || <center>[[585]]</center> || <center>[[730]]</center> || <center>891</center> || 1068 || 1261 || {{OEIS2C|A051870}} || [https://oeis.org/A051870/b051870.txt  Table of n, a(n) for n = 0..]

|-
| <center>十九角数</center> ||style="text-align:left" | (17''n''<sup>2</sup> − 15''n'')/2 || <center>[[1]]</center> || [[19]] || [[54]] || [[106]] || [[175]] || [[261]] || [[364]] || [[484]] || <center>[[621]]</center> || <center>[[775]]</center> || <center>[[946]]</center> || [[1134]] || 1339 || {{OEIS2C|A051871}} || [https://oeis.org/A051871/b051871.txt  Table of n, a(n) for n = 0..]

|-
| <center>二十角数</center> ||style="text-align:left" | 9''n''<sup>2</sup> − 8''n'' || <center>[[1]]</center> || [[20]] || [[57]] || [[112]] || [[185]] || [[276]] || [[385]] || [[512]] || <center>[[657]]</center> || <center>[[820]]</center> || [[1001]] || [[1200]] || 1417 || {{OEIS2C|A051872}} || [https://oeis.org/A051872/b051872.txt  Table of n, a(n) for n = 0..]

|-
| 二十一角数 ||style="text-align:left" | (19''n''<sup>2</sup> − 17''n'')/2 || <center>[[1]]</center> || [[21]] || [[60]] || [[118]] || [[195]] || [[291]] || [[406]] || [[540]] || <center>[[693]]</center> || <center>[[865]]</center> || 1056 || 1266 || 1495 || {{OEIS2C|A051873}} || [https://oeis.org/A051873/b051873.txt  Table of n, a(n) for n = 0..]

|-
| 二十二角数 ||style="text-align:left" | 10''n''<sup>2</sup> − 9''n'' || <center>[[1]]</center> || [[22]] || [[63]] || [[124]] || [[205]] || [[306]] || [[427]] || [[568]] || <center>[[729]]</center> || <center>[[910]]</center> || [[1111]] || [[1332]] || 1573 || {{OEIS2C|A051874}} || [https://oeis.org/A051874/b051874.txt  Table of n, a(n) for n = 0..]

|-
| 二十三角数 ||style="text-align:left" | (21''n''<sup>2</sup> − 19''n'')/2 || <center>[[1]]</center> || [[23]] || [[66]] || [[130]] || [[215]] || [[321]] || [[448]] || [[596]] || <center>[[765]]</center> || <center>955</center> || 1166 || 1398 || 1651 || {{OEIS2C|A051875}} || [https://oeis.org/A051875/b051875.txt  Table of n, a(n) for n = 0..]

|-
| 二十四角数 ||style="text-align:left" | 11''n''<sup>2</sup> − 10''n'' || <center>[[1]]</center> || [[24]] || [[69]] || [[136]] || [[225]] || [[336]] || [[469]] || [[624]] || <center>[[801]]</center> || [[1000]] || 1221 || 1464 || [[1729]] || {{OEIS2C|A051876}} || [https://oeis.org/A051876/b051876.txt  Table of n, a(n) for n = 0..]

|-
| 二十五角数 ||style="text-align:left" | (23''n''<sup>2</sup> − 21''n'')/2 || <center>[[1]]</center> || [[25]] || [[72]] || [[142]] || [[235]] || [[351]] || [[490]] || [[652]] || <center>837</center> || 1045 || 1276 || 1530 || 1807 || {{OEIS2C|A255184}} || [https://oeis.org/A255184/b255184.txt  Table of n, a(n) for n = 0..]

|-
| 二十六角数 ||style="text-align:left" | 12''n''<sup>2</sup> − 11''n'' || <center>[[1]]</center> || [[26]] || [[75]] || [[148]] || [[245]] || [[366]] || [[511]] || [[680]] || <center>873</center> || [[1090]] || [[1331]] || 1596 || 1885 || {{OEIS2C|A255185}} || [https://oeis.org/A255185/b255185.txt  Table of n, a(n) for n = 0..]

|-
| 二十七角数 ||style="text-align:left" | (25''n''<sup>2</sup> − 23''n'')/2 || <center>[[1]]</center> || [[27]] || [[78]] || [[154]] || [[255]] || [[381]] || [[532]] || [[708]] || <center>909</center> || 1135 || 1386 || 1662 || 1963 || {{OEIS2C|A255186}} || [https://oeis.org/A255186/b255186.txt  Table of n, a(n) for n = 0..]

|-
| 二十八角数 ||style="text-align:left" | 13''n''<sup>2</sup> − 12''n'' || <center>[[1]]</center> || [[28]] || [[81]] || [[160]] || [[265]] || [[396]] || [[553]] || [[736]] || <center>[[945]]</center> || 1180 || [[1441]] || [[1728]] || 2041 || {{OEIS2C|A161935}} || [https://oeis.org/A161935/b161935.txt  Table of n, a(n) for n = 0..]

|-
| 二十九角数 ||style="text-align:left" | (27''n''<sup>2</sup> − 25''n'')/2 || <center>[[1]]</center> || [[29]] || [[84]] || [[166]] || [[275]] || [[411]] || [[574]] || 764 || <center>981</center> || [[1225]] || 1496 || 1794 || 2119 || {{OEIS2C|A255187}} || [https://oeis.org/A255187/b255187.txt  Table of n, a(n) for n = 0..]

|-
| <center>三十角数</center> ||style="text-align:left" | 14''n''<sup>2</sup> − 13''n'' || <center>[[1]]</center> || [[30]] || [[87]] || [[172]] || [[285]] || [[426]] || [[595]] || [[792]] || 1017 || 1270 || 1551 || 1860 || [[2197]] || {{OEIS2C|A254474}} || [https://oeis.org/A254474/b254474.txt  Table of n, a(n) for n = 0..]

|}

== 関連項目 ==
* [[図形数]]
* [[正多角形]]
* [[中心つき多角数]]
* [[六芒星数]]

== 外部リンク ==
* {{MathWorld|title=Polygonal Number|urlname=PolygonalNumber}}
* [http://www.virtuescience.com/polygonal-numbers.html PolygonalNumbers virtuescience 多角数表]

{{級数}}

{{Normdaten}}
{{DEFAULTSORT:たかくすう}}
[[Category:多角数|*]]
[[Category:多角形]]
[[Category:数学に関する記事]]