A360897 - OEIS

%I #9 Feb 25 2023 08:41:15

%S 1,1,1,1,1,0,-2,-5,-9,-8,7,48,120,161,-18,-798,-2486,-4088,-692,19840,

%T 71159,130467,31737,-688014,-2644266,-5066453,-866551,31217375,

%U 121457519,231494879,-10834753,-1756652362,-6638239650,-12044755426,5372265122,117373545212

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

%F a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} (-1)^k * binomial(n-1-3*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)\4, (-1)^j*binomial(i-1-3*j, j)*v[i-3*j])); v;

%Y Cf. A360894, A360896.

%Y Cf. A360886.

%K sign

%O 0,7

%A _Seiichi Manyama_, Feb 25 2023