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A045834
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Half of theta series of cubic lattice with respect to edge.
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2
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
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REFERENCES
| J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 107.
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LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
| 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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PROG
| (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
| A005876(n)=2*a(n).
Sequence in context: A021877 A200623 A201296 * A106148 A192038 A046577
Adjacent sequences: A045831 A045832 A045833 * A045835 A045836 A045837
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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