A104276 Number of partitions of n in which both even and odd squares occur with multiplicity 1. There is no restriction on the parts which are twice even squares.
1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 1, 2, 1, 0, 2, 3, 1, 0, 2, 3, 1, 0, 2, 5, 3, 0, 2, 5, 3, 0, 3, 6, 4, 1, 4, 7, 4, 1, 4, 9, 6, 1, 4, 10, 7, 1, 5, 12, 9, 2, 6, 13, 9, 2, 6, 15, 12, 3, 6, 17, 14, 3, 8, 20, 16, 4, 9, 21, 17, 5, 10, 25, 22, 7, 10, 27, 24, 7, 12, 32, 28, 9, 14, 34, 30, 10, 15, 39, 37
Offset: 0
Keywords
Examples
E.g. a(30) = 3 because we can write 30 as 25+4+1 = 16+9+4+1 = 8+8+9+4+1.
Programs
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Maple
series(product((1+x^((2*k-1)^2)))/(1-x^((2*k)^2)),k=1..100),x=0,100);
Formula
G.f.: Product_{k>0} ((1+x^(2k-1)^2)/(1-x^(2k)^2) = Product_{k>0} ((1+x^(2k-1)^2)*(1+x^(2k)^2)))/(1-x^2(2k)^2).