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A333174
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a(n) = Sum_{k=0..n} r_4(k^2 + 1), where r_4(k) is the number of ways of writing k as a sum of 4 squares (A000118).
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1
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8, 32, 80, 224, 368, 704, 1008, 1752, 2424, 3432, 4248, 5736, 7176, 9768, 11352, 14088, 16152, 20472, 23944, 28312, 31528, 37576, 42280, 50056, 54680, 62216, 67640, 78296, 85880, 96008, 103784, 116552, 126968, 142808, 152888, 167624, 178008, 197880, 212616, 230904
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n) ~ (40*G/Pi^2) * n^3, where G is Catalan's constant (A006752).
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EXAMPLE
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a(0) = r_4(0^2 + 1) = r_4(1) = A000118(1) = 8.
a(1) = r_4(0^2 + 1) + r_4(1^1 + 1) = r_4(1) + r_4(2) = A000118(1) + A000118(2) = 8 + 24 = 32.
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MATHEMATICA
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Accumulate @ Table[SquaresR[4, k^2 + 1], {k, 0, 100}]
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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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