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 A360150 #20 Apr 09 2024 09:25:14
%S A360150 1,2,6,21,77,288,1090,4159,15964,61557,238221,924597,3597290,14024341,
%T A360150 54770176,214218966,838959762,3289471537,12910910288,50720828034,
%U A360150 199422778415,784672001097,3089564308849,12172411084432,47984843655991,189260578353602
%N A360150 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-k,n-3*k).
%F A360150 G.f.: 1 / ( sqrt(1-4*x) * (1 - x^3 * c(x)^5) ), where c(x) is the g.f. of A000108.
%F A360150 a(n) ~ 2^(2*n+1) / sqrt(Pi*n). - _Vaclav Kotesovec_, Jan 28 2023
%F A360150 D-finite with recurrence n*a(n) +2*(-7*n+6)*a(n-1) +2*(36*n-61)*a(n-2) +4*(-41*n+103)*a(n-3) +(161*n-530)*a(n-4) +(-71*n+278)*a(n-5) +6*(2*n-9)*a(n-6)=0. - _R. J. Mathar_, Mar 12 2023
%F A360150 a(n) = [x^n] 1/(((1-x)^2-x^3) * (1-x)^(n-1)). - _Seiichi Manyama_, Apr 09 2024
%p A360150 A360150 := proc(n)
%p A360150 add(binomial(2*n-k,n-3*k),k=0..n/3) ;
%p A360150 end proc:
%p A360150 seq(A360150(n),n=0..70) ; # _R. J. Mathar_, Mar 12 2023
%t A360150 a[n_] := Sum[Binomial[2*n - k, n - 3*k], {k, 0, Floor[n/3]}]; Array[a, 26, 0] (* _Amiram Eldar_, Jan 28 2023 *)
%o A360150 (PARI) a(n) = sum(k=0, n\3, binomial(2*n-k, n-3*k));
%o A360150 (PARI) my(N=30, x='x+O('x^N)); Vec(1/(sqrt(1-4*x)*(1-x^3*(2/(1+sqrt(1-4*x)))^5)))
%Y A360150 Cf. A105872, A144904, A360151, A360152, A360153, A360168.
%Y A360150 Cf. A000108.
%K A360150 nonn
%O A360150 0,2
%A A360150 _Seiichi Manyama_, Jan 28 2023