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 A117572 #18 Jan 11 2025 18:15:17
%S A117572 1,0,3,1,3,3,4,3,6,4,6,6,7,6,9,7,9,9,10,9,12,10,12,12,13,12,15,13,15,
%T A117572 15,16,15,18,16,18,18,19,18,21,19,21,21,22,21,24,22,24,24,25,24,27,25,
%U A117572 27,27,28,27,30,28,30,30,31,30,33,31,33,33,34,33,36,34,36,36,37,36,39,37
%N A117572 Expansion of (1 + 2*x^2)/((1 - x^2)*(1 - x^3)).
%C A117572 Diagonal sums of A110128 [this cross-reference is wrong - _N. J. A. Sloane_, Jan 01 2008]. Partial sums are A117573.
%H A117572 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,0,-1).
%F A117572 a(n) = a(n-2)+a(n-3)-a(n-5).
%F A117572 a(n) = cos(2*Pi*n/3+Pi/3)/3-sin(2*Pi*n/3+Pi/3)/sqrt(3)+3(-1)^n/4+(6n+7)/12.
%F A117572 a(n) = Sum_{k=0..floor(n/2)} 2*A001045(L((n-2k+2)/3)) where L(j/p) is the Legendre symbol of j and p.
%o A117572 (Maxima) a(n):=(n+1)/2+3/4*(-1)^n+1/12-(1/3)*(-2)^fix(mod(n,3)/2); /* _Tani Akinari_, Nov 10 2012 */
%K A117572 easy,nonn
%O A117572 0,3
%A A117572 _Paul Barry_, Mar 29 2006