A131996 Number of partitions of n into distinct powers of 2 or of 3.
1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 12
Offset: 1
Keywords
Examples
a(10) = #{9+1,8+2,4+3+2+1}=3;
a(20) = #{16+4,16+3+1,9+8+3,9+8+2+1}=4;
a(30) = #{27+3,27+2+1,16+9+4+1,16+9+3+2,16+8+4+2,16+8+3+2+1}=6.
Links
- R. Zumkeller, Table of n, a(n) for n = 1..1000
Programs
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Maple
g:=(product((1+x^(2^k))*(1+x^(3^k)),k=0..10))/(1+x): gser:=series(g,x=0,111): seq(coeff(gser,x,n),n=1..108); # Emeric Deutsch, Aug 26 2007
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Mathematica
max = 100; Product[((1 + x^(2^k)) (1 + x^(3^k))), {k, 0, Log[2, max] // Ceiling}]/(1 + x) + O[x]^max // CoefficientList[#, x]& // Rest (* Jean-François Alcover, Sep 30 2016 *)
Formula
G.f.: Product_{k>=0} ((1+x^(2^k))(1+x^(3^k)))/(1+x) (offset 0). - Emeric Deutsch, Aug 26 2007
Comments