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Search: id:A028625
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| A028625 |
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Expansion of (theta_3(z)*theta_3(15z)+theta_2(z)*theta_2(15z)). |
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1
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| 1, 2, 0, 0, 6, 0, 4, 0, 0, 2, 4, 0, 0, 0, 0, 2, 10, 0, 0, 4, 0, 0, 0, 0, 8, 2, 0, 0, 0, 0, 0, 4, 0, 0, 8, 0, 6, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 2, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 6, 4, 0, 0, 14, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 12, 0, 0, 4, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 12, 0, 0, 0, 6, 0, 0, 0
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Theta series of quadratic form (or lattice) with Gram matrix [ 2, 1; 1, 8 ].
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LINKS
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John Cannon, Table of n, a(n) for n = 0..5000
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FORMULA
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Expansion of phi(q)phi(q^15) +4q^4*psi(q^2)psi(q^30) in powers of q where phi(),psi() are Ramanujan theta functions. - Michael Somos Aug 26 2006
Expansion of (eta(q^3)eta(q^5))^2/(eta(q)eta(q^15)) +(eta(q)eta(q^15))^2/(eta(q^3)eta(q^5)) in powers of q. - Michael Somos Aug 26 2006
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EXAMPLE
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1 + 2*q^2 + 6*q^8 + 4*q^12 + 2*q^18 + 4*q^20 + 2*q^30 + 10*q^32 + 4*q^38 + 8*q^48 + 2*q^50 + 4*q^62 + 8*q^68 + 6*q^72 + 8*q^80 + 8*q^92 + 2*q^98 + ...
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PROGRAM
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(PARI) {a(n)=if(n<1, n==0, qfrep([2, 1; 1, 8], n, 1)[n]*2)} /* Michael Somos Aug 26 2006 */
(PARI) {a(n)=if(n<1, n==0, sumdiv(n, d, kronecker(-15, d) +kronecker(d, 3)*kronecker(n/d, 5) ))} /* Michael Somos Aug 26 2006 */
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CROSSREFS
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Adjacent sequences: A028622 A028623 A028624 this_sequence A028626 A028627 A028628
Sequence in context: A094785 A035536 A098643 this_sequence A045866 A112964 A128613
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KEYWORD
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nonn
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AUTHOR
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njas
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