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 A112553 #22 Feb 16 2024 09:56:24
%S A112553 1,1,-1,-2,0,2,1,-1,-1,0,0,0,1,1,-1,-2,0,2,1,-1,-1,0,0,0,1,1,-1,-2,0,
%T A112553 2,1,-1,-1,0,0,0,1,1,-1,-2,0,2,1,-1,-1,0,0,0,1,1,-1,-2,0,2,1,-1,-1,0,
%U A112553 0,0,1,1,-1,-2,0,2,1,-1,-1,0,0,0
%N A112553 Expansion of 1/( (1+x^2)*(1-x+x^2) ).
%C A112553 Row sums of A112552.
%H A112553 G. C. Greubel, <a href="/A112553/b112553.txt">Table of n, a(n) for n = 0..1000</a>
%H A112553 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,-2,1,-1).
%F A112553 a(n) = (1/4)*Sum_{k=0..n} (-1)^floor((n-k)/2)*Sum_{j=0..n} (1+(-1)^(n-j))*(1+(-1)^(j-k)) *binomial((j+k)/2, k).
%F A112553 From _G. C. Greubel_, Jan 13 2022: (Start)
%F A112553 a(n) = Sum_{k=0..n} (-1)^floor((n-k)/2)*((1 + (-1)^(n+k))/2)*binomial((n+k+2)/2, k+1).
%F A112553 a(n + 12) = a(n). (End)
%F A112553 a(n) = -a(-4-n) for all n in Z. - _Michael Somos_, Feb 15 2024
%e A112553 G.f. = 1 + x - x^2 - 2*x^3 + 2*x^5 + x^6 - x^7 - x^8 + x^12 + x^13 - x^14 - 2*x^15 + ... - _Michael Somos_, Feb 15 2024
%t A112553 Join[{1}, PadRight[{}, 120, {1,-1,-2,0,2,1,-1,-1,0,0,0,1}]] (* _G. C. Greubel_, Jan 13 2022 *)
%t A112553 a[ n_] := {1, 1, -1, -2, 0, 2, 1, -1, -1, 0, 0, 0}[[1 + Mod[n, 12]]]; (* _Michael Somos_, Feb 15 2024 *)
%o A112553 (PARI) {a(n) = [1, 1, -1, -2, 0, 2, 1, -1, -1, 0, 0, 0][1 + n%12]}; /* _Michael Somos_, Feb 15 2024 */
%Y A112553 Cf. A010892, A112552, A112554.
%K A112553 easy,sign
%O A112553 0,4
%A A112553 _Paul Barry_, Sep 13 2005