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A028594
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Expansion of (theta_3(z)*theta_3(7z)+theta_2(z)*theta_2(7z))^2.
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2
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1, 4, 12, 16, 28, 24, 48, 4, 60, 52, 72, 48, 112, 56, 12, 96, 124, 72, 156, 80, 168, 16, 144, 96, 240, 124, 168, 160, 28, 120, 288, 128, 252, 192, 216, 24, 364, 152, 240, 224, 360, 168, 48, 176, 336, 312, 288, 192
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Theta series of square of Kleinian lattice Z[ (-1+sqrt(-7))/2 ].
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FORMULA
| a(n)=4b(n) where b(n) is multiplicative and b(p^e) = 1, if p=7, b(p^e) = (p^(e+1)-1)/(p-1) otherwise.
G.f.: (theta_3(z)*theta_3(7z) + theta_2(z)*theta_2(7z))^2.
G.f. is square of g.f. of A002652.
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PROG
| (PARI) a(n)=if(n<1, n==0, 4*sigma(n/7^valuation(n, 7))) /* Michael Somos Oct 07 2005 */
(PARI) a(n)=if(n<1, n==0, 2*qfrep([2, 1, 0, 0; 1, 4, 0, 0; 0, 0, 2, 1; 0, 0, 1, 4], n, 1)[n]) /* Michael Somos Oct 07 2005 */
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CROSSREFS
| Sequence in context: A187084 A090818 A075191 * A152680 A066632 A038242
Adjacent sequences: A028591 A028592 A028593 * A028595 A028596 A028597
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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