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A303666 Expansion of 1/((1 - x)*(1 - Sum_{k>=0} x^(2^k))). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partial sums of A023359.

LINKS

Table of n, a(n) for n=0..38.

Index entries for sequences related to compositions

MAPLE

b:= proc(n) option remember;

      `if`(n=0, 1, add(b(n-2^i), i=0..ilog2(n)))

    end:

a:= proc(n) option remember;

      `if`(n<0, 0, b(n)+a(n-1))

    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}]]

CROSSREFS

Cf. A000079, A000123, A023359, A209229.

Sequence in context: A136299 A208354 A003116 * A260917 A165648 A287381

Adjacent sequences:  A303663 A303664 A303665 * A303667 A303668 A303669

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 28 2018

STATUS

approved

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Last modified July 16 09:13 EDT 2020. Contains 335784 sequences. (Running on oeis4.)