A172033 Number of partitions of n into distinct parts that are 1 or even, i.e., into distinct terms of A004277.
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 8, 8, 10, 10, 12, 12, 15, 15, 18, 18, 22, 22, 27, 27, 32, 32, 38, 38, 46, 46, 54, 54, 64, 64, 76, 76, 89, 89, 104, 104, 122, 122, 142, 142, 165, 165, 192, 192, 222, 222, 256, 256, 296, 296, 340, 340, 390, 390, 448, 448
Offset: 0
Keywords
Examples
a(12) = #{12, 10+2, 8+4, 6+4+2} = 4;
a(13) = #{12+1, 10+2+1, 8+4+1, 6+4+2+1} = 4;
a(14) = #{14, 12+2, 10+4, 8+6, 8+4+2} = 5.
Crossrefs
Cf. A025065.
Programs
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PARI
my(N=68, q='q+O('q^N)); Vec( (1+q)*prod(n=1,N,1+q^(2*n)) ) \\ Joerg Arndt, Mar 11 2014
Formula
G.f.: (1+q) * Product_{n>=1} (1 + q^(2*n)). - Joerg Arndt, Mar 11 2014
Comments