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G.f. A(x) satisfies A(x) = 1 / (1 - x - x^2 * A(x^3)).
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%I #10 Dec 04 2023 06:49:14

%S 1,1,2,3,5,9,15,26,46,79,138,241,418,729,1270,2209,3849,6703,11669,

%T 20325,35393,61629,107329,186900,325464,566779,986987,1718745,2993062,

%U 5212135,9076470,15805899,27524544,47931568,83468632,145353195,253119779,440785795

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

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

%p A367666 := proc(n)

%p option remember;

%p if n = 0 then

%p 1;

%p else

%p procname(n-1) + add(procname(k) * procname(n-2-3*k),k=0..floor((n-2)/3)) ;

%p end if;

%p end proc:

%p seq(A367666(n),n=0..70) ; # _R. J. Mathar_, Dec 04 2023

%o (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;

%Y Cf. A367659, A367667.

%Y Cf. A319436.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 26 2023