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A333047 Number of compositions of 2n into n powers of 2.

%I A333047 #16 Mar 28 2022 08:13:25
%S A333047 1,1,1,4,13,31,76,218,645,1849,5281,15346,44980,131704,385568,1131874,
%T A333047 3331429,9819405,28977079,85633438,253424053,750895163,2227288196,
%U A333047 6613217348,19654450476,58463536356,174041552556,518488451716,1545686334184,4610827520500
%N A333047 Number of compositions of 2n into n powers of 2.
%H A333047 Alois P. Heinz, <a href="/A333047/b333047.txt">Table of n, a(n) for n = 0..2078</a>
%F A333047 a(n) = A073266(2n,n).
%F A333047 a(n) mod 2 = 1 <=> n in { A003714 }.
%F A333047 a(n) ~ c * d^n / sqrt(n), where d = 3.03557496500556374352187743150809307334142929675774277... and c = 0.257758082536856928607441503594486605201517917904563... - _Vaclav Kotesovec_, Mar 10 2020
%e A333047 a(3) = 4: 222, 114, 141, 411.
%e A333047 a(4) = 13: 2222, 1124, 1142, 1214, 1241, 1412, 1421, 2114, 2141, 2411, 4112, 4121, 4211.
%p A333047 b:= proc(n, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
%p A333047       `if`(t=0, 0, add(b(n-2^j, t-1), j=0..ilog2(n))))
%p A333047     end:
%p A333047 a:= n-> b(2*n, n):
%p A333047 seq(a(n), n=0..30);
%t A333047 b[n_, t_] := b[n, t] = If[n == 0, If[t == 0, 1, 0], If[t == 0, 0, Sum[b[n - 2^j, t - 1], {j, 0, Floor@Log2[n]}]]];
%t A333047 a[n_] := b[2*n, n];
%t A333047 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Mar 28 2022, after _Alois P. Heinz_ *)
%Y A333047 Cf. A003714, A073266.
%K A333047 nonn
%O A333047 0,4
%A A333047 _Alois P. Heinz_, Mar 06 2020