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Search: id:A023919
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| A023919 |
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Theta series of A*_7 lattice. Expansion of F_8(q^2). |
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4
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| 1, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 56, 0, 0, 112, 126, 0, 0, 0, 0, 0, 0, 336, 0, 0, 0, 0, 576, 0, 0, 672, 756, 0, 0, 0, 0, 0, 0, 1232, 0, 0, 0, 0, 1512, 0, 0, 2016, 2072, 0, 0, 0, 0, 0, 0, 2800, 0, 0, 0, 0, 4032, 0, 0, 4048, 4158, 0, 0, 0, 0, 0, 0, 5712, 0, 0, 0, 0, 5544, 0, 0, 6944, 7560
(list; graph; listen)
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OFFSET
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0,8
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REFERENCES
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S. Ahlgren, The sixth, eighth, ninth and tenth powers of Ramanujan's theta function. Proc. Amer. Math. Soc. 128 (2000), 1333-1338.
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 114.
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LINKS
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G. Nebe and N. J. A. Sloane, Home page for this lattice
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EXAMPLE
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1 + 16*q^7 + 56*q^12 + 112*q^15 + 126*q^16 + 336*q^23 + 576*q^28 + 672*q^31 + 756*q^32 + 1232*q^39 + 1512*q^44 + 2016*q^47 + 2072*q^48 + O(q^49)
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PROGRAM
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(MAGMA) L:=Lattice("A", 7); D:=Dual(L); T1<q> := ThetaSeries(D, 60);
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CROSSREFS
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Cf. A008447 (A_7).
Sequence in context: A072723 A111413 A072838 this_sequence A008433 A010111 A118067
Adjacent sequences: A023916 A023917 A023918 this_sequence A023920 A023921 A023922
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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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