A104277 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 odd squares.
1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 8, 10, 10, 11, 11, 13, 13, 14, 14, 14, 16, 16, 18, 18, 20, 20, 22, 23, 23, 25, 25, 28, 28, 30, 30, 33, 35, 35, 38, 39, 43, 43, 46, 46, 49, 51, 51, 55, 56, 60, 61
Offset: 0
Examples
a(21)=7 because we can write 21 as 18+2+1 = 16+4+1 = 16+2+2+1 = 9+4+2+2+2+2 = 9+2+2+2+2+2+2 = 4+2+2+2+2+2+2+2+2+1 = 2+2+2+2+2+2+2+2+2+2+1.
Programs
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Maple
series(product((1+x^((2*k)^2))/(1-x^((2*k-1)^2)),k=1..100),x=0,100);
Formula
G.f.: Product_{k>0} (1+x^((2*k)^2))/(1-x^((2*k-1)^2)).
Extensions
Missing term a(46) added by Jason Yuen, Jan 20 2025