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
Examples
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.
Links
- David A. Corneth, Table of n, a(n) for n = 0..9999
Programs
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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
Formula
G.f.: (1-x)/Product_{k>=0} (1-x^(2^k))*(1-x^(3^k)). - Emeric Deutsch, Aug 26 2007
Extensions
Prepended a(0) = 1, Joerg Arndt and David A. Corneth, Sep 06 2020