cp's OEIS Frontend

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

%I A131995 #30 Feb 16 2022 09:54:22
%S A131995 1,1,2,3,5,6,9,11,16,20,26,32,42,50,62,74,92,108,131,153,184,213,251,
%T A131995 288,339,387,448,511,589,666,761,857,976,1095,1237,1384,1561,1737,
%U A131995 1946,2161,2415,2672,2971,3281,3640,4007,4425,4860,5359,5869,6446,7049,7729,8428
%N A131995 Number of partitions of n into powers of 2 or of 3.
%H A131995 David A. Corneth, <a href="/A131995/b131995.txt">Table of n, a(n) for n = 0..9999</a>
%F A131995 G.f.: (1-x)/Product_{k>=0} (1-x^(2^k))*(1-x^(3^k)). - _Emeric Deutsch_, Aug 26 2007
%e A131995 a(10) = #{9+1, 8+2, 8+1+1, 4+4+2, 4+4+1+1, 4+3+3, 4+3+2+1,
%e A131995 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,
%e A131995 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,
%e A131995 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,
%e A131995 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.
%p A131995 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
%Y A131995 Cf. A018819, A062051, A023893, A000041, A131996.
%K A131995 nonn,easy
%O A131995 0,3
%A A131995 _Reinhard Zumkeller_, Aug 06 2007
%E A131995 Prepended a(0) = 1, _Joerg Arndt_ and _David A. Corneth_, Sep 06 2020