cp's OEIS Frontend

A131996 Number of partitions of n into distinct powers of 2 or of 3.

%I A131996 #15 Sep 30 2016 12:56:40
%S A131996 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,
%T A131996 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,
%U A131996 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
%N A131996 Number of partitions of n into distinct powers of 2 or of 3.
%C A131996 a(A081601(n+1)) = n+1 and a(m) < n+1 for m < A081601(n+1).
%H A131996 R. Zumkeller, <a href="/A131996/b131996.txt">Table of n, a(n) for n = 1..1000</a>
%F A131996 G.f.: Product_{k>=0} ((1+x^(2^k))(1+x^(3^k)))/(1+x) (offset 0). - _Emeric Deutsch_, Aug 26 2007
%e A131996 a(10) = #{9+1,8+2,4+3+2+1}=3;
%e A131996 a(20) = #{16+4,16+3+1,9+8+3,9+8+2+1}=4;
%e A131996 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.
%p A131996 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
%t A131996 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 *)
%Y A131996 Cf. A000009, A062051, A106244, A131995.
%K A131996 nonn
%O A131996 1,3
%A A131996 _Reinhard Zumkeller_, Aug 06 2007