A131995 Number of partitions of n into powers of 2 or of 3.

1, 1, 2, 3, 5, 6, 9, 11, 16, 20, 26, 32, 42, 50, 62, 74, 92, 108, 131, 153, 184, 213, 251, 288, 339, 387, 448, 511, 589, 666, 761, 857, 976, 1095, 1237, 1384, 1561, 1737, 1946, 2161, 2415, 2672, 2971, 3281, 3640, 4007, 4425, 4860, 5359, 5869, 6446, 7049, 7729, 8428

Offset

0,3

Links

David A. Corneth, Table of n, a(n) for n = 0..9999

Formula

G.f.: (1-x)/Product_{k>=0} (1-x^(2^k))*(1-x^(3^k)). - Emeric Deutsch, Aug 26 2007

Example

a(10) = #{9+1, 8+2, 8+1+1, 4+4+2, 4+4+1+1, 4+3+3, 4+3+2+1,
4+3+1+1+1, 4+2+2+2, 4+2+2+1+1, 4+2+1+1+1+1, 4+1+1+1+1+1+1, 3+3+3+1,
3+3+2+2, 3+3+2+1+1, 3+3+1+1+1+1, 3+2+2+2+1, 3+2+2+1+1+1,
3+2+1+1+1+1+1, 3+1+1+1+1+1+1+1, 2+2+2+2+2, 2+2+2+2+1+1, 2+2+2+1+1+1+1,
2+2+1+1+1+1+1+1, 2+1+1+1+1+1+1+1+1, 1+1+1+1+1+1+1+1+1+1} = 26.

Maple

g:=(1-x)/(product((1-x^(2^k))*(1-x^(3^k)), k=0..10)): gser:=series(g, x=0, 60): seq(coeff(gser, x, n), n=1..53); # Emeric Deutsch, Aug 26 2007

Crossrefs

Cf. A018819, A062051, A023893, A000041, A131996.

Sequence in context: A339277 A027588 A224956 * A363066 A060714 A241819

Adjacent sequences: A131992 A131993 A131994 * A131996 A131997 A131998

Keyword

nonn,easy

Author

Reinhard Zumkeller, Aug 06 2007

Extensions

Prepended a(0) = 1, Joerg Arndt and David A. Corneth, Sep 06 2020

Status

approved