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 A360212 #11 Mar 12 2023 11:11:39
%S A360212 1,2,6,19,67,242,890,3310,12423,46959,178526,681893,2614698,10059000,
%T A360212 38807021,150080294,581649776,2258469988,8783966719,34214789901,
%U A360212 133450049457,521134066663,2037313708685,7972641631438,31228124666374,122421230120657
%N A360212 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n-5*k,n-3*k).
%F A360212 G.f.: 1 / ( sqrt(1-4*x) * (1 + x^3 * c(x)) ), where c(x) is the g.f. of A000108.
%F A360212 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 A360212 A360212 := proc(n)
%p A360212 add((-1)^k*binomial(2*n-5*k,n-3*k),k=0..n/3) ;
%p A360212 end proc:
%p A360212 seq(A360212(n),n=0..70) ; # _R. J. Mathar_, Mar 12 2023
%o A360212 (PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(2*n-5*k, n-3*k));
%o A360212 (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 A360212 Cf. A191993, A307354, A360186.
%Y A360212 Cf. A000108, A360152.
%K A360212 nonn
%O A360212 0,2
%A A360212 _Seiichi Manyama_, Jan 30 2023