A365734 - OEIS

%I #13 Sep 17 2023 10:05:16

%S 1,1,1,1,1,1,2,5,11,21,36,58,94,163,306,599,1170,2229,4140,7596,14002,

%T 26228,49979,96212,185491,356255,681247,1300680,2488500,4782037,

%U 9231306,17875306,34656389,67194497,130263382,252631688,490513867,953923030,1858136173,3624102244

%N G.f. satisfies A(x) = 1 + x*A(x) / (1 - x^5*A(x)^2).

%F a(n) = Sum_{k=0..floor(n/5)} binomial(n-4*k-1,k) * binomial(n-3*k+1,n-5*k) / (n-3*k+1).

%o (PARI) a(n) = sum(k=0, n\5, binomial(n-4*k-1, k)*binomial(n-3*k+1, n-5*k)/(n-3*k+1));

%Y Cf. A212364, A212385, A365735, A365736.

%Y Cf. A365732, A365699.

%K nonn

%O 0,7

%A _Seiichi Manyama_, Sep 17 2023