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A014110
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Number of ordered ways of writing n as a sum of 4 squares of nonnegative integers.
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10
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1, 4, 6, 4, 5, 12, 12, 4, 6, 16, 18, 12, 8, 16, 24, 12, 5, 24, 30, 16, 18, 28, 24, 12, 12, 28, 42, 28, 12, 36, 48, 16, 6, 36, 42, 36, 29, 28, 48, 28, 18, 48, 60, 28, 24, 60, 48, 24, 8, 44, 72, 48, 30, 48, 84, 36, 24, 52, 54
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OFFSET
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0,2
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COMMENTS
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This counts ordered sums of squares of nonnegative integers, whereas A000118 counts ordered sums of squares of integers of any sign. - R. J. Mathar, May 16 2023
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LINKS
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FORMULA
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Coefficient of q^n in (1/16)*(1 + theta_3(0, q))^4; or coeff. of q^n in (Sum q^(i^2), i=0..inf)^4.
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EXAMPLE
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a(1)=4 counts 0^2+0^2+0^2+1^2 = 0^2+0^2+1^2+0^2 = 0^2+1^2+0^2+0^2 = 1^2+0^2+0^2+0^2. a(2)=6 counts 0^2+0^2+1^2+1^2 = 0^2+1^2+0^2+1^2 = 0^2+1^2+1^2+0^2 = 1^2+0^2+0^2+1^2 = 1^2+0^2+1^2+0^2 = 1^2+1^2+0^2+0^2. - R. J. Mathar, May 16 2023
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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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Joe Keane (jgk(AT)jgk.org)
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STATUS
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approved
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