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A188671
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A000145(n) / 8 - (n^5 + 1).
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0
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1, 0, -24, -32, 108, 275, -176, -1056, 45, 3157, 1080, -6541, -836, 16839, 2072, -33824, 1188, 67100, 1672, -95883, 19162, 161083, -8208, -224653, 2707, 371325, 67500, -520025, -1188, 870551, 8512, -1082400, 148334, 1419889, 10428, -1588228
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OFFSET
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1,3
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COMMENTS
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Theorem 2 in the Hales reference defines t_p = (n_p - 8(p^5 + 1)) / (32 p^(5/2)) where n_p is the number of ways to express p as a sum of 12 squares.
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LINKS
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FORMULA
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G.f.: ((Sum_{k} x^k^2)^12 - 1) / 8 - (2*x + 21*x^2 + 76*x^3 + 16*x^4 + 6*x^5 - x^6) / (1 - x)^6.
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EXAMPLE
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x - 24*x^3 - 32*x^4 + 108*x^5 + 275*x^6 - 176*x^7 - 1056*x^8 + 45*x^9 + ...
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PROG
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(PARI) {a(n) = if( n<1, 0, polcoeff( sum( k = 1, sqrtint(n), 2 * x^k^2, 1 + x*O(x^n))^12, n) / 8 - (n^5 + 1))}
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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