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%I #11 Dec 20 2023 10:40:04
%S 1,2,4,7,13,23,41,72,128,226,400,706,1248,2204,3894,6877,12149,21459,
%T 37907,66957,118275,208919,369037,651863,1151453,2033921,3592719,
%U 6346167,11209863,19801075,34976589,61782572,109132628,192771658,340511506,601478868,1062451154,1876711698,3315020026
%N Expansion of 1/((1 - x)*(1 - Sum_{k>=0} x^(2^k))).
%C Partial sums of A023359.
%H Alois P. Heinz, <a href="/A303666/b303666.txt">Table of n, a(n) for n = 0..2000</a>
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%p a:= proc(n) option remember; 1+
%p `if`(n>0, add(a(n-2^i), i=0..ilog2(n)), 0)
%p end:
%p seq(a(n), n=0..50); # _Alois P. Heinz_, Apr 28 2018
%t nmax = 38; CoefficientList[Series[1/((1 - x) (1 - Sum[x^2^k, {k, 0, nmax}])), {x, 0, nmax}], x]
%t a[0] = 1; a[n_] := a[n] = Sum[Boole[k == 2^IntegerExponent[k, 2]] a[n - k], {k, 1, n}]; Accumulate[Table[a[n], {n, 0, 38}]]
%Y Cf. A000079, A000123, A023359, A209229.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Apr 28 2018
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