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A236930
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Number of integer solutions to a^2 + b^2 + c^2 + 5*d^2 = n.
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10
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1, 6, 12, 8, 6, 26, 36, 24, 28, 42, 72, 72, 8, 48, 108, 48, 54, 64, 84, 120, 26, 72, 144, 88, 84, 126, 216, 80, 24, 180, 156, 192, 92, 96, 288, 144, 42, 144, 240, 144, 168, 252, 144, 168, 72, 182, 396, 184, 72, 258, 372, 192, 48, 208, 360, 312, 252, 160, 360, 360, 48
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: theta_3(q)^3*theta_3(q^5), where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Aug 01 2018
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MAPLE
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MATHEMATICA
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For number of solutions to a^2+b^2+c^2+k*d^2=n for k=1, 2, 3, 4, 5, 6, 7, 8, 12 see A000118, A236928, A236926, A236923, A236930, A236931, A236932, A236927, A236933.
Join[{1}, Table[Length[Reduce[a^2+b^2+c^2+5d^2==n, {a, b, c, d}, Integers]], {n, 60}]] (* Harvey P. Dale, Jul 02 2017 *)
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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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