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 A375315 #15 Aug 12 2024 10:21:40
%S A375315 1,1,1,4,7,11,23,45,81,154,296,555,1046,1986,3753,7085,13404,25348,
%T A375315 47904,90568,171245,323728,612009,1157071,2187496,4135527,7818464,
%U A375315 14781237,27944604,52830706,99879234,188826693,356986401,674901117,1275934888,2412219633,4560424135
%N A375315 Expansion of (1 + x)/(1 - x^2*(1 + x)^3).
%H A375315 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,3,3,1).
%F A375315 a(n) = a(n-2) + 3*a(n-3) + 3*a(n-4) + a(n-5).
%F A375315 a(n) = Sum_{k=0..floor(n/2)} binomial(3*k+1,n-2*k).
%F A375315 a(n) = A116090(n) + A116090(n-1).
%o A375315 (PARI) my(N=40, x='x+O('x^N)); Vec((1+x)/(1-x^2*(1+x)^3))
%o A375315 (PARI) a(n) = sum(k=0, n\2, binomial(3*k+1, n-2*k));
%Y A375315 Cf. A093040, A375316.
%Y A375315 Cf. A116090, A375317.
%K A375315 nonn
%O A375315 0,4
%A A375315 _Seiichi Manyama_, Aug 12 2024