A339447 G.f.: Sum_{k>=0} x^(2^k) / Product_{j=1..2^k} (1 - x^j).

0, 1, 2, 2, 4, 4, 6, 7, 11, 12, 17, 20, 27, 32, 42, 50, 66, 78, 99, 119, 150, 179, 223, 267, 329, 393, 480, 572, 695, 826, 995, 1181, 1417, 1674, 1997, 2355, 2796, 3288, 3887, 4558, 5370, 6281, 7371, 8603, 10067, 11719, 13674, 15886, 18486, 21432, 24879, 28787, 33344

Offset

0,3

Comments

Number of partitions of n such that the number of parts is a power of 2.

Also number of partitions of n such that the largest part is a power of 2.

Links

Table of n, a(n) for n=0..52.

Index entries for sequences related to partitions

Example

a(6) = 6 because we have [6], [5, 1], [4, 2], [3, 3], [3, 1, 1, 1] and [2, 2, 1, 1] (see the first comment) or [4, 2], [4, 1, 1], [2, 2, 2], [2, 2, 1, 1], [2, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1] (see the second comment).

Mathematica

nmax = 52; CoefficientList[Series[Sum[x^(2^k)/Product[1 - x^j, {j, 1, 2^k}], {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]

Crossrefs

Cf. A000079, A018819.

Sequence in context: A261797 A067590 A058686 * A027188 A363213 A089076

Adjacent sequences: A339444 A339445 A339446 * A339448 A339449 A339450

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 05 2020

Status

approved