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 A375319 #10 Aug 12 2024 09:32:52
%S A375319 1,1,0,1,4,6,5,8,21,36,45,66,128,224,330,497,851,1452,2287,3556,5826,
%T A375319 9693,15624,24807,40126,65737,106584,171112,276160,448980,728201,
%U A375319 1174985,1897380,3074733,4982688,8055918,13020029,21074012,34125561,55210580,89284541
%N A375319 Expansion of (1 + x)/(1 - x^3*(1 + x)^3).
%H A375319 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,3,3,1).
%F A375319 a(n) = a(n-3) + 3*a(n-4) + 3*a(n-5) + a(n-6).
%F A375319 a(n) = Sum_{k=0..floor(n/3)} binomial(3*k+1,n-3*k).
%o A375319 (PARI) my(N=50, x='x+O('x^N)); Vec((1+x)/(1-x^3*(1+x)^3))
%o A375319 (PARI) a(n) = sum(k=0, n\3, binomial(3*k+1, n-3*k));
%Y A375319 Cf. A115055, A375321.
%K A375319 nonn
%O A375319 0,5
%A A375319 _Seiichi Manyama_, Aug 12 2024