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A104277
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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.
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0
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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, 30, 30, 33, 35, 35, 38, 39, 43, 43, 46, 46, 49, 51, 51, 55, 56, 60, 61
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OFFSET
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0,5
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LINKS
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FORMULA
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G.f.: product_{k>0}((1+x^(2k)^2))/(1-x^(2k-1)^2)).
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EXAMPLE
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E.g. 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.
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MAPLE
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series(product((1+x^((2*k)^2))/(1-x^((2*k-1)^2)), k=1..100), x=0, 100);
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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