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Search: id:A028641
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| A028641 |
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Expansion of (theta_3(z)*theta_3(19z)+theta_2(z)*theta_2(19z)). |
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1
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| 1, 2, 0, 0, 2, 4, 0, 4, 0, 2, 0, 4, 0, 0, 0, 0, 2, 4, 0, 2, 4, 0, 0, 4, 0, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, 8, 2, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 4, 0, 6, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 4, 0, 4, 2, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 2, 8, 0, 0, 4, 2, 0, 4, 0, 8, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 6, 4, 0, 0, 0
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Theta series of quadratic form with Gram matrix [ 2, 1; 1, 10 ].
Expansion of phi(q)* phi(q^19) +4*q^5* psi(q^2)* psi(q^38) in powers of q where phi(), psi() are Ramanujan theta functions. - Michael Somos Feb 27 2007
Moebius transform is period 19 sequence [ 2, -2, -2, 2, 2, 2, 2, -2, 2, -2, 2, -2, -2, -2, -2, 2, 2, -2, 0, ...]. - Michael Somos Feb 27 2007
a(n)=2*b(n) where b(n) is multiplicative and b(19^e) = 1, b(p^e) = e+1 if kronecker(-19, p) = 1, b(p^e) = (1+(-1)^e)/2 if kronecker(-19, p) = -1. - Michael Somos Feb 27 2007
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PROGRAM
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(PARI) {a(n)=if(n<1, n==0, sumdiv(n, d, kronecker(-19, d))*2)} /* Michael Somos Feb 27 2007 */
(PARI) {a(n)=if(n<1, n==0, qfrep([2, 1; 1, 10], n, 1)[n]*2)} /* Michael Somos Feb 27 2007 */
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CROSSREFS
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Sequence in context: A020474 A135589 A158122 this_sequence A141416 A127862 A024690
Adjacent sequences: A028638 A028639 A028640 this_sequence A028642 A028643 A028644
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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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