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 A371842 #7 Apr 08 2024 09:21:05
%S A371842 1,3,10,36,133,498,1882,7161,27391,105210,405499,1567332,6072724,
%T A371842 23578221,91712089,357301827,1393986898,5445422340,21296030401,
%U A371842 83370591273,326688422203,1281227165640,5028742763407,19751799462378,77632592859316,305316702610581
%N A371842 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-2*k+1,n-3*k).
%F A371842 a(n) = [x^n] 1/((1-x-x^3) * (1-x)^(n+1)).
%F A371842 From _Vaclav Kotesovec_, Apr 08 2024: (Start)
%F A371842 Recurrence: (n-1)*a(n) = (9*n-11)*a(n-1) - 2*(11*n-16)*a(n-2) + (9*n-13)*a(n-3) - 2*(2*n-3)*a(n-4).
%F A371842 G.f.: 2 / (4*x^2 + 3*x*sqrt(1-4*x) - 9*x + 2).
%F A371842 a(n) ~ 2^(2*n+3) / (3*sqrt(Pi*n)). (End)
%o A371842 (PARI) a(n) = sum(k=0, n\3, binomial(2*n-2*k+1, n-3*k));
%Y A371842 Cf. A105872.
%K A371842 nonn
%O A371842 0,2
%A A371842 _Seiichi Manyama_, Apr 08 2024