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Search: id:A005879
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| A005879 |
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Theta series of D_4 lattice with respect to deep hole.
(Formerly M4509)
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+0
4
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| 8, 32, 48, 64, 104, 96, 112, 192, 144, 160, 256, 192, 248, 320, 240, 256, 384, 384, 304, 448, 336, 352, 624, 384, 456, 576, 432, 576, 640, 480, 496, 832, 672, 544, 768, 576, 592, 992, 768, 640, 968, 672, 864, 960, 720, 896, 1024, 960, 784, 1248, 816, 832, 1536
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Expansion of Jacobi theta_2(q)^4/(2q) in powers of q^2. - Michael Somos Apr 11 2004
Expansion of q^(-1/2)8(eta(q^2)^2/eta(q))^4 in powers of q. - Michael Somos Apr 11 2004
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 118.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..10000
G. Nebe and N. J. A. Sloane, Home page for this lattice
Index entries for sequences related to D_4 lattice
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FORMULA
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G.f.: 8(Product_{k>0} (1-x^k)(1+x^k)^2)^4. - Michael Somos Apr 11 2004
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PROGRAM
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(PARI) a(n)=if(n<0, 0, 8*sigma(2*n+1))
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CROSSREFS
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A008438(n)=a(n)/8. A005880(n)=a(n)/4. A000118(2n+1)=-A096727(2n+1)=a(n).
Sequence in context: A144096 A127988 A129749 this_sequence A067519 A009245 A018842
Adjacent sequences: A005876 A005877 A005878 this_sequence A005880 A005881 A005882
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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