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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	`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 = 4q^(1/2) + 8q^(5/2) + 4q^(9/2) + 8q^(13/2) + 8*q^(17/2) + ...`
	PROGRAM	`(PARI) {a(n)=if(n<0, 0, n=4n+1; 4sumdiv(n, d, (-1)^(d\2)))} /* Michael Somos Oct 31 2006 */`
	CROSSREFS	`A008441(n)=a(n)/4.` `Sequence in context: A019838 A010713 A105398 this_sequence A055026 A059163 A091198` `Adjacent sequences: A005880 A005881 A005882 this_sequence A005884 A005885 A005886`
	KEYWORD	`nonn`
	AUTHOR	`njas`
	EXTENSIONS	`corrected by njas. Latt 21, p 25.`

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Last modified September 5 01:44 EDT 2008. Contains 143476 sequences.

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