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.
%I A101180 #24 Aug 16 2025 18:08:53
%S A101180 0,8,671,15639,42159,981911,77624048,1807894920,4873553880,
%T A101180 113507005568,8973184757831,208989037004319,563373081435879,
%U A101180 13121182828725551,1037282211558181688,24158714697817430640,65124801462951244560,1516782492521509296728
%N A101180 Numbers n such that 19*n^2 + 19*n + 1 is a square.
%C A101180 Define a(1)=0, a(2)=8, a(3)=671, a(4)=15639, a(5)=42159, a(6)=981911, the first 6 terms found for the sequence then a(7)=57799*(2*a(3)+1)-a(2)-1, a(8)=57799*(2*a(4)+1)-a(1)-1 for n>8 a(n)=57799*(2*a(n-4)+1)-a(n-8)-1 remark:57799 = 38*39*39+1 =2*19*(39^2)+1
%H A101180 Harvey P. Dale, <a href="/A101180/b101180.txt">Table of n, a(n) for n = 1..790</a>
%H A101180 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,115598,-115598,0,0,-1,1).
%F A101180 G.f.: -x^2*(8*x^6+663*x^5+14968*x^4+26520*x^3+14968*x^2+663*x+8) / ((x-1)*(x^4-340*x^2+1)*(x^4+340*x^2+1)). - _Colin Barker_, Mar 05 2013
%t A101180 CoefficientList[Series[-x^2(8x^6+663x^5+14968x^4+26520x^3+14968x^2+663x+8)/((x-1)(x^4-340x^2+1)(x^4+340x^2+1)),{x,0,30}],x] (* or *) LinearRecurrence[{1,0,0,115598,-115598,0,0,-1,1},{0,0,8,671,15639,42159,981911,77624048,1807894920},30] (* _Harvey P. Dale_, Aug 16 2025 *)
%Y A101180 Cf. A105839.
%K A101180 nonn,easy
%O A101180 1,2
%A A101180 _Pierre CAMI_, Apr 06 2005, Apr 22 2005
%E A101180 Edited by _N. J. A. Sloane_, Aug 29 2008 at the suggestion of R. J. Mathar
%E A101180 More terms (using recursive formula in comment) from _Jon E. Schoenfield_, Jul 10 2010
%E A101180 a(18) from _Colin Barker_, Mar 05 2013