cp's OEIS Frontend

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.

%I A104277 #11 Jan 20 2025 09:03:25
%S A104277 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,
%T A104277 14,14,14,16,16,18,18,20,20,22,23,23,25,25,28,28,30,30,33,35,35,38,39,
%U A104277 43,43,46,46,49,51,51,55,56,60,61
%N 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.
%F A104277 G.f.: Product_{k>0} (1+x^((2*k)^2))/(1-x^((2*k-1)^2)).
%e A104277 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.
%p A104277 series(product((1+x^((2*k)^2))/(1-x^((2*k-1)^2)),k=1..100),x=0,100);
%K A104277 easy,nonn
%O A104277 0,5
%A A104277 _Noureddine Chair_, Mar 01 2005
%E A104277 Missing term a(46) added by _Jason Yuen_, Jan 20 2025