cp's OEIS Frontend

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

%I A367666 #10 Dec 04 2023 06:49:14
%S A367666 1,1,2,3,5,9,15,26,46,79,138,241,418,729,1270,2209,3849,6703,11669,
%T A367666 20325,35393,61629,107329,186900,325464,566779,986987,1718745,2993062,
%U A367666 5212135,9076470,15805899,27524544,47931568,83468632,145353195,253119779,440785795
%N A367666 G.f. A(x) satisfies A(x) = 1 / (1 - x - x^2 * A(x^3)).
%F A367666 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..floor((n-2)/3)} a(k) * a(n-2-3*k).
%p A367666 A367666 := proc(n)
%p A367666     option remember;
%p A367666     if n = 0 then
%p A367666         1;
%p A367666     else
%p A367666         procname(n-1) + add(procname(k) * procname(n-2-3*k),k=0..floor((n-2)/3)) ;
%p A367666     end if;
%p A367666 end proc:
%p A367666 seq(A367666(n),n=0..70) ; # _R. J. Mathar_, Dec 04 2023
%o A367666 (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 A367666 Cf. A367659, A367667.
%Y A367666 Cf. A319436.
%K A367666 nonn
%O A367666 0,3
%A A367666 _Seiichi Manyama_, Nov 26 2023