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A339365
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Number of partitions of n into an odd number of squares.
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6
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0, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 3, 2, 3, 3, 3, 4, 5, 4, 6, 5, 7, 7, 7, 8, 10, 9, 12, 10, 14, 13, 14, 15, 18, 17, 21, 20, 24, 24, 25, 27, 31, 30, 35, 34, 40, 40, 42, 45, 50, 50, 56, 55, 64, 65, 68, 72, 78, 79, 88, 85, 99, 99, 105, 110, 118, 122, 131, 132, 146, 149
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OFFSET
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0,10
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LINKS
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FORMULA
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G.f.: (1/2) * (Product_{k>=1} 1 / (1 - x^(k^2)) - Product_{k>=1} 1 / (1 + x^(k^2))).
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EXAMPLE
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a(9) = 3 because we have [9], [4, 4, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1].
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MATHEMATICA
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nmax = 70; CoefficientList[Series[(1/2) (Product[1/(1 - x^(k^2)), {k, 1, Floor[nmax^(1/2)] + 1}] - Product[1/(1 + x^(k^2)), {k, 1, Floor[nmax^(1/2)] + 1}]), {x, 0, nmax}], x]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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