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A005883 Theta series of square lattice with respect to deep hole.
(Formerly M3319)
+0
5
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)
OFFSET

0,1

REFERENCES

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.

FORMULA

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

EXAMPLE

Theta = 4*q^(1/2) + 8*q^(5/2) + 4*q^(9/2) + 8*q^(13/2) + 8*q^(17/2) + ...

PROGRAM

(PARI) {a(n)=if(n<0, 0, n=4*n+1; 4*sumdiv(n, d, (-1)^(d\2)))} /* Michael Somos Oct 31 2006 */

CROSSREFS

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

KEYWORD

nonn

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

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Last modified November 25 08:46 EST 2009. Contains 167481 sequences.


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