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 A373905 #13 Jun 22 2024 14:12:27
%S A373905 1,1,1,2,8,29,86,224,554,1381,3556,9382,24901,65737,172321,450017,
%T A373905 1174985,3072365,8044478,21074012,55199573,144535714,378366976,
%U A373905 990441502,2592800365,6787973872,17771619370,46527959417,121813193825,318910531073,834913179137
%N A373905 a(n) = Sum_{k=0..floor(n/3)} binomial(n+3*k,n-3*k).
%H A373905 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,21,-15,6,-1).
%F A373905 a(n) = 6*a(n-1) - 15*a(n-2) + 21*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).
%F A373905 G.f.: 1/(1 - x - x^3/(1 - x)^5).
%o A373905 (PARI) a(n) = sum(k=0, n\3, binomial(n+3*k,n-3*k));
%Y A373905 Cf. A000930, A005251, A024493, A099099, A369845.
%Y A373905 Cf. A107025, A373904, A373906.
%K A373905 nonn,easy
%O A373905 0,4
%A A373905 _Seiichi Manyama_, Jun 22 2024