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Search: id:A005883
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| A005883 |
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Theta series of square lattice with respect to deep hole.
(Formerly M3319)
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+0
5
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| 4, 8, 4, 8, 8, 0, 12, 8, 0, 8, 8, 8, 4, 8, 0, 8, 16, 0, 8, 0, 4, 16, 8, 0, 8, 8, 0, 8, 8, 8, 4, 16, 0, 0, 8, 0, 16, 8, 8, 8, 0, 0, 12, 8, 0, 8, 16, 0, 8, 8, 0, 16, 0, 0, 0, 16, 12, 8, 8, 0, 8, 8, 0, 0, 8, 8, 16, 8, 0, 8, 8, 0, 12, 8, 0, 0, 16, 0, 8, 8, 0, 24, 0, 8, 8, 0, 0, 8, 8, 0, 4, 16, 8, 8, 16, 0, 0
(list; graph; listen)
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OFFSET
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0,1
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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. 106.
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FORMULA
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Expansion of Jacobi theta constant q^(-1/2)*theta_2(z/2)^2. - Michael Somos Oct 31 2006
G.f.: 4*(Product_{k>0} (1-x^k)*(1+x^(2k))^2)^2 . - Michael Somos Oct 31 2006
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EXAMPLE
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Theta = 4*q^(1/2) + 8*q^(5/2) + 4*q^(9/2) + 8*q^(13/2) + 8*q^(17/2) + ...
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PROGRAM
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(PARI) {a(n)=if(n<0, 0, n=4*n+1; 4*sumdiv(n, d, (-1)^(d\2)))} /* Michael Somos Oct 31 2006 */
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CROSSREFS
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A008441(n)=a(n)/4.
Sequence in context: A155970 A010713 A105398 this_sequence A055026 A059163 A091198
Adjacent sequences: A005880 A005881 A005882 this_sequence A005884 A005885 A005886
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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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