%I #12 Feb 26 2023 06:56:10

%S 1,1,1,1,0,-2,-5,-8,-5,13,57,117,110,-179,-1089,-2591,-2852,4370,

%T 30383,77884,88638,-165233,-1133248,-2963659,-3172087,8519500,

%U 53092522,135857134,122296383,-543728791,-2983007603,-7219203443,-4427302115,40439842811,194091075002

%N G.f. satisfies A(x) = 1 + x/(1 + x^3) * A(x/(1 + x^3)).

%H Seiichi Manyama, <a href="/A360898/b360898.txt">Table of n, a(n) for n = 0..1000</a>

%F a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} (-1)^k * binomial(n-1-2*k,k) * a(n-1-3*k).

%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\3, (-1)^j*binomial(i-1-2*j, j)*v[i-3*j])); v;

%Y Cf. A172385, A360899.

%Y Cf. A360890.

%K sign

%O 0,6

%A _Seiichi Manyama_, Feb 25 2023