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A374157
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a(n) = (-1)^floor(n/2)*n.
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3
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0, 1, -2, -3, 4, 5, -6, -7, 8, 9, -10, -11, 12, 13, -14, -15, 16, 17, -18, -19, 20, 21, -22, -23, 24, 25, -26, -27, 28, 29, -30, -31, 32, 33, -34, -35, 36, 37, -38, -39, 40, 41, -42, -43, 44, 45, -46, -47, 48, 49, -50, -51, 52, 53, -54, -55, 56, 57, -58, -59
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OFFSET
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0,3
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COMMENTS
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For all odd numbers n (A005408) and all whole numbers z (A001057) K(z/n) = K(a(n)/z), where K(z/n) denotes the Kronecker symbol (A372728). This fact is equivalent to the law of quadratic reciprocity and its first and second supplement.
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n) = Pi/4 - log(2)/2 = A196521.
a(n) = [x^n] -x*(x^2 + 2*x - 1)/(x^2 + 1)^2.
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MAPLE
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a := n -> (-1)^iquo(n, 2)*n: seq(a(n), n = 0..59);
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MATHEMATICA
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PROG
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(Python)
def A374157(n): return (-1)**(n // 2)*n
(Python)
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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