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 A375364 #12 Aug 13 2024 11:40:36
%S A375364 1,-1,2,1,3,4,12,17,35,67,127,234,451,850,1602,3031,5740,10837,20490,
%T A375364 38751,73253,138471,261814,494972,935738,1769079,3344568,6323022,
%U A375364 11953992,22599700,42725842,80775309,152709941,288705926,545813095,1031887517,1950836006
%N A375364 Expansion of 1/( (1 + x) * (1 - x^2*(1 + x)^3) ).
%H A375364 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-1,1,4,6,4,1).
%F A375364 a(n) = -a(n-1) + a(n-2) + 4*a(n-3) + 6*a(n-4) + 4*a(n-5) + a(n-6).
%F A375364 a(n) = Sum_{k=0..floor(n/2)} binomial(3*k-1,n-2*k).
%F A375364 a(n) = A375365(n) + A375365(n-1).
%o A375364 (PARI) my(N=40, x='x+O('x^N)); Vec(1/((1+x)*(1-x^2*(1+x)^3)))
%o A375364 (PARI) a(n) = sum(k=0, n\2, binomial(3*k-1, n-2*k));
%Y A375364 Cf. A375315, A375317, A375365.
%K A375364 sign
%O A375364 0,3
%A A375364 _Seiichi Manyama_, Aug 13 2024