A365697 - OEIS

%I #9 Sep 16 2023 10:40:50

%S 1,0,0,0,1,1,1,1,4,8,13,19,38,79,153,273,509,999,1979,3818,7331,14279,

%T 28189,55599,109275,215165,426093,846638,1683215,3348212,6673679,

%U 13333171,26679522,53437369,107151335,215154204,432586412,870678377,1754094266

%N G.f. satisfies A(x) = 1 + x^4*A(x)^3 / (1 - x*A(x)).

%F a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k-1,n-4*k) * binomial(n-k+1,k) / (n-k+1).

%o (PARI) a(n) = sum(k=0, n\4, binomial(n-3*k-1, n-4*k)*binomial(n-k+1, k)/(n-k+1));

%Y Cf. A023427, A215341, A215342, A357308, A365696.

%Y Cf. A365245.

%K nonn

%O 0,9

%A _Seiichi Manyama_, Sep 16 2023