A304908 Expansion of x * (d/dx) 1/(1 - Sum_{k>=0} x^(2^k)).

0, 1, 4, 9, 24, 50, 108, 217, 448, 882, 1740, 3366, 6504, 12428, 23660, 44745, 84352, 158270, 296064, 551950, 1026360, 1903524, 3522596, 6504998, 11990160, 22061700, 40528748, 74343096, 136183488, 249145148, 455265420, 830985473, 1515201792, 2760087990, 5023154832, 9133857670

Offset

0,3

Comments

Sum of all parts of all compositions (ordered partitions) of n into powers of 2.

Links

Table of n, a(n) for n=0..35.

Index entries for sequences related to compositions

Formula

a(n) = n*A023359(n).

Mathematica

nmax = 35; CoefficientList[Series[x D[1/(1 - Sum[x^2^k, {k, 0, Floor[Log[nmax]/Log[2]] + 1}]), x], {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[Boole[k == 2^IntegerExponent[k, 2]] a[n - k], {k, 1, n}]; Table[n a[n], {n, 0, 35}]

Crossrefs

Cf. A000079, A001787, A023359, A036987, A281811, A304797, A303666, A304909.

Sequence in context: A158141 A056575 A056032 * A127979 A112262 A077922

Adjacent sequences: A304905 A304906 A304907 * A304909 A304910 A304911

Keyword

nonn

Author

Ilya Gutkovskiy, May 20 2018

Status

approved