A303666 Expansion of 1/((1 - x)*(1 - Sum_{k>=0} x^(2^k))).

1, 2, 4, 7, 13, 23, 41, 72, 128, 226, 400, 706, 1248, 2204, 3894, 6877, 12149, 21459, 37907, 66957, 118275, 208919, 369037, 651863, 1151453, 2033921, 3592719, 6346167, 11209863, 19801075, 34976589, 61782572, 109132628, 192771658, 340511506, 601478868, 1062451154, 1876711698, 3315020026

Offset: 0

Author

Ilya Gutkovskiy, Apr 28 2018

Keywords

• nonn

Comments

Partial sums of A023359.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000
• Index entries for sequences related to compositions

Crossrefs

Cf. A000079, A000123, A023359, A209229.

Programs

Maple

a:= proc(n) option remember; 1+
     `if`(n>0, add(a(n-2^i), i=0..ilog2(n)), 0)
    end:
seq(a(n), n=0..50);  # Alois P. Heinz, Apr 28 2018

Mathematica

nmax = 38; CoefficientList[Series[1/((1 - x) (1 - Sum[x^2^k, {k, 0, nmax}])), {x, 0, nmax}], x]
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}]]