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Search: id:A034598
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| A034598 |
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Second coefficient of extremal theta series of even unimodular lattice in dimension 24n. |
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+0
4
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| 1, 16773120, 39007332000, 15281788354560, 2972108280960000, 406954241261568000, 45569082381053868000, 4499117081888292864000, 408472720963469499617280, 34975479259332252426240000
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Although these initially increase, they eventually go negative at about term 1700 (i.e. dimension about 40800) - see references.
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REFERENCES
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J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag.
C. L. Mallows, A. M. Odlyzko and N. J. A. Sloane, "Upper bounds for modular forms, lattices and codes", J. Alg., 36 (1975), 68-76.
C. L. Mallows and N. J. A. Sloane, An Upper Bound for Self-Dual Codes, Information and Control, 22 (1973), 188-200.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 0..100
G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998 (Abstract, pdf, ps).
N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
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EXAMPLE
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When n=1 we get the theta series of the 24-dimensional Leech lattice: 1+196560*q^4+16773120*q^6+... (see A008408). For n=2 we get A004672 and for n=3, A004675.
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MAPLE
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For Maple program see A034597.
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CROSSREFS
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Cf. A034597 (leading coefficient).
Sequence in context: A004673 A058909 A105650 this_sequence A011574 A022540 A057070
Adjacent sequences: A034595 A034596 A034597 this_sequence A034599 A034600 A034601
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KEYWORD
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nonn
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AUTHOR
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njas
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