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 A375317 #12 Mar 25 2025 10:15:12
%S A375317 1,2,2,5,11,18,34,68,126,235,450,851,1601,3032,5739,10838,20489,38752,
%T A375317 73252,138472,261813,494973,935737,1769080,3344567,6323023,11953991,
%U A375317 22599701,42725841,80775310,152709940,288705927,545813094,1031887518,1950836005,3688154521
%N A375317 Expansion of (1 + x)^2/(1 - x^2*(1 + x)^3).
%H A375317 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,3,3,1).
%F A375317 a(n) = a(n-2) + 3*a(n-3) + 3*a(n-4) + a(n-5).
%F A375317 a(n) = Sum_{k=0..floor(n/2)} binomial(3*k+2,n-2*k).
%F A375317 a(n) = A375315(n) + A375315(n-1).
%t A375317 CoefficientList[Series[(1+x)^2/(1-x^2(1+x)^3),{x,0,40}],x] (* or *) LinearRecurrence[{0,1,3,3,1},{1,2,2,5,11},40] (* _Harvey P. Dale_, Mar 25 2025 *)
%o A375317 (PARI) my(N=40, x='x+O('x^N)); Vec((1+x)^2/(1-x^2*(1+x)^3))
%o A375317 (PARI) a(n) = sum(k=0, n\2, binomial(3*k+2, n-2*k));
%Y A375317 Cf. A116090, A375315.
%K A375317 nonn
%O A375317 0,2
%A A375317 _Seiichi Manyama_, Aug 12 2024