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Search: id:A030640
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| A030640 |
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Discriminant of lattice A_n of determinant n+1. |
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+0
2
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| 1, 1, -3, -2, 5, 3, -7, -4, 9, 5, -11, -6, 13, 7, -15, -8, 17, 9, -19, -10, 21, 11, -23, -12, 25, 13, -27, -14, 29, 15, -31, -16, 33, 17, -35, -18, 37, 19, -39, -20, 41, 21, -43, -22, 45, 23, -47, -24, 49, 25, -51, -26, 53, 27, -55, -28, 57, 29, -59
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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J. H. Conway, Sensual Quadratic Form, MAA, p. 4.
G. L. Watson, Integral Quadratic Forms, Camb., p. 2.
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FORMULA
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a(2n) = (-1)^n*(2*n+1), a(2n+1) = (-1)^n*(n+1). Or (apart from signs), a(n) = n, n odd; n/2, n even.
G.f.: (1+x-x^2)/(1+x^2)^2 - Len Smiley (smiley(AT)math.uaa.alaska.edu).
a(-2-n)=(-1)^n*a(n). - Michael Somos Jun 15 2005
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PROGRAM
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(PARI) a(n)=if(n==-1, 0, (-1)^(n\2)*(n+1)/gcd(n+1, 2)) /* Michael Somos Jun 15 2005 */
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CROSSREFS
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A026741 is unsigned version: a(n)=(-1)^[n/2]A026741(n+1).
Sequence in context: A124332 A165342 A076605 this_sequence A145051 A026741 A105658
Adjacent sequences: A030637 A030638 A030639 this_sequence A030641 A030642 A030643
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KEYWORD
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sign,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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