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 A360186 #24 Mar 12 2023 12:58:31
%S A360186 1,2,6,19,68,246,905,3364,12624,47715,181392,692808,2656441,10219208,
%T A360186 39423792,152461079,590861182,2294182428,8922674221,34754402618,
%U A360186 135552346392,529335200219,2069344561102,8097878381208,31718268482881,124341261876650
%N A360186 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n-6*k,n-3*k).
%H A360186 Seiichi Manyama, <a href="/A360186/b360186.txt">Table of n, a(n) for n = 0..1000</a>
%F A360186 G.f.: 1 / ( sqrt(1-4*x) * (1 + x^3) ).
%F A360186 a(n) ~ 2^(2*n + 6) / (65*sqrt(Pi*n)). - _Vaclav Kotesovec_, Jan 29 2023
%F A360186 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
%F A360186 a(n)+a(n-3) = A000984(n). - _R. J. Mathar_, Mar 12 2023
%p A360186 A360186 := proc(n)
%p A360186 add((-1)^k*binomial(2*n-6*k,n-3*k),k=0..n/3) ;
%p A360186 end proc:
%p A360186 seq(A360186(n),n=0..70) ; # _R. J. Mathar_, Mar 12 2023
%t A360186 Table[Sum[(-1)^k Binomial[2n-6k,n-3k],{k,0,Floor[n/3]}],{n,0,30}] (* _Harvey P. Dale_, Mar 05 2023 *)
%o A360186 (PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(2*n-6*k, n-3*k));
%o A360186 (PARI) my(N=30, x='x+O('x^N)); Vec(1/(sqrt(1-4*x)*(1+x^3)))
%Y A360186 Cf. A054108, A360185.
%Y A360186 Cf. A000984, A360153.
%K A360186 nonn,easy
%O A360186 0,2
%A A360186 _Seiichi Manyama_, Jan 29 2023