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Search: id:A023917
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| A023917 |
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Theta series of A*_5 lattice. |
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+0
2
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| 1, 0, 0, 0, 0, 12, 0, 0, 30, 20, 0, 0, 30, 0, 0, 0, 0, 120, 0, 0, 132, 60, 0, 0, 90, 0, 0, 0, 0, 180, 0, 0, 270, 180, 0, 0, 140, 0, 0, 0, 0, 480, 0, 0, 420, 132, 0, 0, 270, 0, 0, 0, 0, 420, 0, 0, 600, 420, 0, 0, 360, 0, 0, 0, 0, 960, 0, 0, 840, 360, 0, 0, 330, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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Expansion of Ahlgren's F_6(q^2).
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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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John Cannon, Table of n, a(n) for n = 0..10000
G. Nebe and N. J. A. Sloane, Home page for this lattice
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EXAMPLE
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1 + 12*q^5 + 30*q^8 + 20*q^9 + 30*q^12 + 120*q^17 + 132*q^20 + 60*q^21 + 90*q^24 + 180*q^29 + 270*q^32 + 180*q^33 + 140*q^36 + 480*q^41 + 420*q^44 + 132*q^45 + 270*q^48 + 420*q^53 + 600*q^56 + 420*q^57 + 360*q^60 + O(q^61)
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PROGRAM
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(MAGMA) L:=Lattice("A", 5); D:=Dual(L); T1<q> := ThetaSeries(D, 120);
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CROSSREFS
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Sequence in context: A104203 A004012 A072837 this_sequence A064141 A156401 A048730
Adjacent sequences: A023914 A023915 A023916 this_sequence A023918 A023919 A023920
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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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