A367666 G.f. A(x) satisfies A(x) = 1 / (1 - x - x^2 * A(x^3)).

1, 1, 2, 3, 5, 9, 15, 26, 46, 79, 138, 241, 418, 729, 1270, 2209, 3849, 6703, 11669, 20325, 35393, 61629, 107329, 186900, 325464, 566779, 986987, 1718745, 2993062, 5212135, 9076470, 15805899, 27524544, 47931568, 83468632, 145353195, 253119779, 440785795

Offset: 0

Author

Seiichi Manyama, Nov 26 2023

Keywords

• nonn

Crossrefs

Cf. A367659, A367667.

Cf. A319436.

Programs

Maple

A367666 := proc(n)
    option remember;
    if n = 0 then
        1;
    else
        procname(n-1) + add(procname(k) * procname(n-2-3*k),k=0..floor((n-2)/3)) ;
    end if;
end proc:
seq(A367666(n),n=0..70) ; # R. J. Mathar, Dec 04 2023

PARI

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

Formula

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..floor((n-2)/3)} a(k) * a(n-2-3*k).