cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A261276 100-gonal numbers: a(n) = 98*n*(n-1)/2 + n.

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%I A261276 #37 Aug 11 2025 23:12:38
%S A261276 0,1,100,297,592,985,1476,2065,2752,3537,4420,5401,6480,7657,8932,
%T A261276 10305,11776,13345,15012,16777,18640,20601,22660,24817,27072,29425,
%U A261276 31876,34425,37072,39817,42660,45601,48640,51777,55012,58345,61776,65305,68932,72657,76480
%N A261276 100-gonal numbers: a(n) = 98*n*(n-1)/2 + n.
%C A261276 According to the common formula for the polygonal numbers: (s-2)*n*(n-1)/2 + n (here s = 100).
%H A261276 Kelvin Voskuijl, <a href="/A261276/b261276.txt">Table of n, a(n) for n = 0..10000</a>
%H A261276 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%H A261276 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A261276 a(n) = n*(49*n - 48).
%F A261276 G.f.: x*(1+97*x)/(1-x)^3. [_Bruno Berselli_, Aug 20 2015]
%F A261276 E.g.f.: exp(x)*(x + 49*x^2). - _Nikolaos Pantelidis_, Feb 12 2023
%p A261276 A261276:=seq((98*n*(n-1))/2 + n,n=0..10^2); # _Muniru A Asiru_, Sep 27 2017
%t A261276 Table[n (49 n - 48), {n, 0, 40}] (* _Bruno Berselli_, Aug 20 2015 *)
%t A261276 PolygonalNumber[100,Range[0,40]] (* Requires Mathematica version 10 or later *) (* or *) LinearRecurrence[{3,-3,1},{0,1,100},50] (* _Harvey P. Dale_, Jan 04 2019 *)
%o A261276 (JavaScript) function a(n){return 98*n*(n-1)/2+n}
%o A261276 (PARI) first(m)=vector(m,i,i--;98*i*(i-1)/2 + i) \\ _Anders Hellström_, Aug 20 2015
%o A261276 (GAP)
%o A261276 A261276:=List([0..10^2],n->(98*n*(n-1))/2 + n); # _Muniru A Asiru_, Sep 27 2017
%Y A261276 Cf. A167149, A195163, A249911.
%K A261276 nonn,easy
%O A261276 0,3
%A A261276 _Sergey Pavlov_, Aug 13 2015