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Search: id:A028997
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| A028997 |
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Theta series of quadratic form with Gram matrix [ 4, 1, 0, 1; 1, 4, 1, 0; 0, 1, 4, -1; 1, 0, -1, 4 ]. |
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+0
2
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| 1, 0, 8, 8, 16, 8, 24, 0, 40, 16, 40, 16, 72, 24, 8, 32, 80, 16, 88, 24, 104, 8, 80, 32, 152, 48, 88, 48, 16, 48, 160, 48, 168, 64, 128, 8, 224, 48, 136, 64, 232, 48, 24, 48, 208, 104, 160, 80, 328, 0, 200, 112, 248, 64, 272, 96, 40, 112, 192, 88, 416, 72, 208, 16, 336, 112, 320
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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M. Koike, Matheiu group M24 and modular forms, Nagoya Math. J., 99 (1985), 147-157. MR0805086 (87e:11060)
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LINKS
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John Cannon, Table of n, a(n) for n = 0..5000
G. Nebe and N. J. A. Sloane, Home page for this lattice
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FORMULA
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Associated with permutations in Mathieu group M24 of shape (14)(7)(2)(1).
G.f. is Fourier series of a weight 2 level 14 modular form. f(-1/ (14 t)) = 14 (t/i)^2 f(t) where q = exp(2 pi i t).
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EXAMPLE
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1 + 8*q^4 + 8*q^6 + 16*q^8 + 8*q^10 + 24*q^12 + 40*q^16 + 16*q^18 + 40*q^20 + ...
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PROGRAM
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(PARI) {a(n) = local(A, B); if( n<0, 0, A = x * O(x^n); B = eta(x^2 + A) * eta(x^14 + A); A = eta(x + A) * eta(x^7 + A); polcoeff( A^4 / B^2 + 4 * x * A * B + 8 * x^2 * B^4 / A^2, n))} /* Michael Somos Nov 22 2007 */
(PARI) {a(n) = local(A); if( n<0, 0, A = [ 4, 1, 0, 1; 1, 4, 1, 0; 0, 1, 4, -1; 1, 0, -1, 4 ]; polcoeff( 1 + 2 * x * Ser(qfrep( A, n, 1)), n))} /* Michael Somos Nov 22 2007 */
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CROSSREFS
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Convolution of A030187 and A134782.
Sequence in context: A001732 A109540 A040057 this_sequence A112439 A022091 A145909
Adjacent sequences: A028994 A028995 A028996 this_sequence A028998 A028999 A029000
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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