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Search: id:A045834
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| A045834 |
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Half of theta series of cubic lattice with respect to edge. |
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+0
3
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| 1, 4, 5, 4, 8, 8, 5, 12, 8, 4, 16, 12, 9, 12, 8, 12, 16, 16, 8, 16, 17, 8, 24, 8, 8, 28, 16, 12, 16, 20, 13, 24, 24, 8, 16, 16, 16, 28, 24, 12, 32, 16, 13, 28, 8, 20, 32, 32, 8, 20, 24, 16, 40, 16, 16, 32, 25, 20, 24, 24, 24, 28, 24, 8, 32, 36, 16, 44, 16, 12, 40, 32, 17, 36, 32
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 107.
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FORMULA
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Euler transform of period 4 sequence [ 4, -5, 4, -3,...]. - Michael Somos Feb 28 2006
Expansion of theta_2(q^2)^2(theta_3(q)+theta_4(q))/(8q) in powers of q^4. - Michael Somos Feb 28 2006
Expansion of q^(-1/4)eta(q^2)^9/(eta(q)^4*eta(q^4)^2) in powers of q. - Michael Somos Feb 28 2006
G.f.: Product_{k>0} (1+x^k)^4*(1-x^(2k))^3/(1+x^(2k))^2 . - Michael Somos Feb 28 2006
Expansion of phi(q)^2*psi(q^2) in powers of q where phi(),psi() are Ramanujan theta functions. - Michael Somos Oct 25 2006
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^9/ eta(x+A)^4/eta(x^4+A)^2, n))} /* Michael Somos Feb 28 2006 */
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CROSSREFS
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A005876(n)=2*a(n).
Sequence in context: A010664 A074967 A021877 this_sequence A106148 A046577 A075464
Adjacent sequences: A045831 A045832 A045833 this_sequence A045835 A045836 A045837
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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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