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 A360153 #17 Mar 12 2023 11:27:49
%S A360153 1,2,6,21,72,258,945,3504,13128,49565,188260,718560,2753721,10588860,
%T A360153 40835160,157871241,611669250,2374441380,9233006541,35956933050,
%U A360153 140220970200,547490880981,2140055896770,8373651697800,32795094564081,128550662334522
%N A360153 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-6*k,n-3*k).
%F A360153 G.f.: 1 / ( sqrt(1-4*x) * (1 - x^3) ).
%F A360153 a(n) ~ 2^(2*n + 6) / (63 * sqrt(Pi*n)). - _Vaclav Kotesovec_, Jan 28 2023
%F A360153 a(n)-a(n-3) = A000984(n). - _R. J. Mathar_, Mar 12 2023
%F A360153 D-finite with recurrence n*a(n) +2*(-2*n+1)*a(n-1) -n*a(n-3) +2*(2*n-1)*a(n-4)=0. - _R. J. Mathar_, Mar 12 2023
%p A360153 A360153 := proc(n)
%p A360153 add(binomial(2*n-6*k,n-3*k),k=0..n/3) ;
%p A360153 end proc:
%p A360153 seq(A360153(n),n=0..70) ; # _R. J. Mathar_, Mar 12 2023
%t A360153 a[n_] := Sum[Binomial[2*n - 6*k, n - 3*k], {k, 0, Floor[n/3]}]; Array[a, 26, 0] (* _Amiram Eldar_, Jan 28 2023 *)
%o A360153 (PARI) a(n) = sum(k=0, n\3, binomial(2*n-6*k, n-3*k));
%o A360153 (PARI) my(N=30, x='x+O('x^N)); Vec(1/(sqrt(1-4*x)*(1-x^3)))
%Y A360153 Cf. A105872, A144904, A360150, A360151, A360152, A360168.
%Y A360153 Cf. A006134, A106188.
%K A360153 nonn
%O A360153 0,2
%A A360153 _Seiichi Manyama_, Jan 28 2023