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 A375275 #11 Aug 09 2024 10:07:33
%S A375275 1,1,0,-5,-13,-12,25,117,196,3,-841,-2200,-2079,4121,19720,33435,1547,
%T A375275 -140772,-372775,-359763,678796,3323203,5702319,437200,-23557759,
%U A375275 -63154959,-62213360,111716475,559940707,972313668,103585625,-3941367643,-10698060204
%N A375275 Expansion of (1 - x + x^2)/(1 - 2*x + 3*x^2 + 2*x^3 + x^4).
%H A375275 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-3,-2,-1).
%F A375275 a(n) = 2*a(n-1) - 3*a(n-2) - 2*a(n-3) - a(n-4).
%F A375275 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(2*n-2*k,2*k).
%o A375275 (PARI) my(N=40, x='x+O('x^N)); Vec((1-x+x^2)/(1-2*x+3*x^2+2*x^3+x^4))
%o A375275 (PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(2*n-2*k, 2*k));
%Y A375275 Cf. A108479, A108480, A108484.
%Y A375275 Cf. A375255.
%K A375275 sign
%O A375275 0,4
%A A375275 _Seiichi Manyama_, Aug 09 2024