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A151759 G.f.: Theta^3, where Theta = Sum_{k>=0} x^(2^k).

%I A151759 #18 Mar 08 2022 10:23:30
%S A151759 0,0,0,1,3,3,4,6,3,3,6,6,4,6,6,0,3,3,6,6,6,6,6,0,4,6,6,0,6,0,0,0,3,3,
%T A151759 6,6,6,6,6,0,6,6,6,0,6,0,0,0,4,6,6,0,6,0,0,0,6,0,0,0,0,0,0,0,3,3,6,6,
%U A151759 6,6,6,0,6,6,6,0,6,0,0,0,6,6,6,0,6,0,0,0,6,0,0,0,0,0,0,0,4,6,6,0,6,0,0,0,6
%N A151759 G.f.: Theta^3, where Theta = Sum_{k>=0} x^(2^k).
%C A151759 Number of ways to write n as an ordered sum of 3 powers of 2. - _Ilya Gutkovskiy_, Feb 02 2021
%H A151759 Seiichi Manyama, <a href="/A151759/b151759.txt">Table of n, a(n) for n = 0..10000</a>
%p A151759 b:= proc(n, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
%p A151759       `if`(t<1, 0, add(b(n-2^j, t-1), j=0..ilog2(n))))
%p A151759     end:
%p A151759 a:= n-> b(n, 3):
%p A151759 seq(a(n), n=0..104);  # _Alois P. Heinz_, Feb 02 2021
%t A151759 b[n_, t_] := b[n, t] = If[n == 0, If[t == 0, 1, 0],
%t A151759      If[t < 1, 0, Sum[b[n - 2^j, t - 1], {j, 0, Floor@Log2[n]}]]];
%t A151759 a[n_] := b[n, 3];
%t A151759 Table[a[n], {n, 0, 104}] (* _Jean-François Alcover_, Mar 08 2022, after _Alois P. Heinz_ *)
%Y A151759 (Sum_{k>=0} x^(2^k))^m; A209229 (m=1), A073267 (m=2), this sequence (m=3), A151760 (m=4), A151761 (m=5), A151762 (m=6).
%Y A151759 Cf. A000079, A151758.
%K A151759 nonn
%O A151759 0,5
%A A151759 _N. J. A. Sloane_, Jun 22 2009