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 A360152 #15 Mar 12 2023 11:25:22
%S A360152 1,2,6,21,73,262,960,3562,13347,50393,191406,730555,2799622,10765092,
%T A360152 41513751,160490906,621805286,2413738744,9385635299,36550685683,
%U A360152 142534105563,556514122937,2175296066129,8511430278018,33334299581686,130662787246407
%N A360152 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-5*k,n-3*k).
%F A360152 G.f.: 1 / ( sqrt(1-4*x) * (1 - x^3 * c(x)) ), where c(x) is the g.f. of A000108.
%F A360152 a(n) ~ 2^(2*n+5) / (31 * sqrt(Pi*n)). - _Vaclav Kotesovec_, Jan 28 2023
%F A360152 D-finite with recurrence 2*n*a(n) +4*(-2*n+1)*a(n-1) +(-3*n+4)*a(n-2) +2*(6*n-11)*a(n-3) +(n-4)*a(n-4) +2*(-n+9)*a(n-5) +4*(-2*n+1)*a(n-6) +(-n+4)*a(n-7) +2*(2*n-9)*a(n-8)=0. - _R. J. Mathar_, Mar 12 2023
%p A360152 A360152 := proc(n)
%p A360152 add(binomial(2*n-5*k,n-3*k),k=0..n/3) ;
%p A360152 end proc:
%p A360152 seq(A360152(n),n=0..70) ; # _R. J. Mathar_, Mar 12 2023
%t A360152 a[n_] := Sum[Binomial[2*n - 5*k, n - 3*k], {k, 0, Floor[n/3]}]; Array[a, 26, 0] (* _Amiram Eldar_, Jan 28 2023 *)
%o A360152 (PARI) a(n) = sum(k=0, n\3, binomial(2*n-5*k, n-3*k));
%o A360152 (PARI) my(N=30, x='x+O('x^N)); Vec(1/(sqrt(1-4*x)*(1-2*x^3/(1+sqrt(1-4*x)))))
%Y A360152 Cf. A105872, A144904, A360150, A360151, A360153.
%Y A360152 Cf. A000108.
%K A360152 nonn
%O A360152 0,2
%A A360152 _Seiichi Manyama_, Jan 28 2023