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 A375321 #9 Aug 12 2024 09:33:01
%S A375321 1,2,1,1,5,10,11,13,29,57,81,111,194,352,554,827,1348,2303,3739,5843,
%T A375321 9382,15519,25317,40431,64933,105863,172321,277696,447272,725140,
%U A375321 1177181,1903186,3072365,4972113,8057421,13038606,21075947,34094041,55199573,89336141
%N A375321 Expansion of (1 + x)^2/(1 - x^3*(1 + x)^3).
%H A375321 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,3,3,1).
%F A375321 a(n) = a(n-3) + 3*a(n-4) + 3*a(n-5) + a(n-6).
%F A375321 a(n) = Sum_{k=0..floor(n/3)} binomial(3*k+2,n-3*k).
%F A375321 a(n) = A375319(n) + A375319(n-1).
%o A375321 (PARI) my(N=40, x='x+O('x^N)); Vec((1+x)^2/(1-x^3*(1+x)^3))
%o A375321 (PARI) a(n) = sum(k=0, n\3, binomial(3*k+2, n-3*k));
%Y A375321 Cf. A115055, A375319.
%Y A375321 Cf. A375317,
%K A375321 nonn
%O A375321 0,2
%A A375321 _Seiichi Manyama_, Aug 12 2024