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 A110513 #19 Sep 11 2024 15:18:04
%S A110513 1,-1,2,-5,11,-24,53,-117,258,-569,1255,-2768,6105,-13465,29698,
%T A110513 -65501,144467,-318632,702765,-1549997,3418626,-7540017,16630031,
%U A110513 -36678688,80897393,-178424817,393528322,-867954037,1914332891,-4222194104,9312342245,-20539017381,45300228866,-99912799977
%N A110513 Expansion of (1 + x)/(1 + 2x + x^3).
%C A110513 Diagonal sums of A110511.
%H A110513 Harvey P. Dale, <a href="/A110513/b110513.txt">Table of n, a(n) for n = 0..1000</a>
%H A110513 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-2,0,-1).
%F A110513 a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..(n-k)} (-1)^(n-k-j)*C(n-k, j)*(-2)^(j-k)*C(k, j-k).
%F A110513 a(0)=1, a(1)=-1, a(2)=2, a(n) = -2*a(n-1) - a(n-3). - _Harvey P. Dale_, Jun 27 2012
%t A110513 CoefficientList[Series[(1+x)/(1+2x+x^3),{x,0,40}],x] (* or *) LinearRecurrence[ {-2,0,-1},{1,-1,2},40] (* _Harvey P. Dale_, Jun 27 2012 *)
%o A110513 (PARI) my(x='x+O('x^50)); Vec((1+x)/(1+2*x+x^3)) \\ _G. C. Greubel_, Aug 29 2017
%Y A110513 A minor variation of A052980.
%K A110513 easy,sign
%O A110513 0,3
%A A110513 _Paul Barry_, Jul 24 2005