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Search: id:A033719
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| A033719 |
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Coefficients in expansion of theta_3(q) * theta_3(q^7). |
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+0
2
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| 1, 2, 0, 0, 2, 0, 0, 2, 4, 2, 0, 4, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 2, 4, 0, 0, 8, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 10, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 2, 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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Number of integer solutions to the equation x^2+7y^2=n.
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REFERENCES
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G. E. Andrews, R. Lewis and Z.-G. Liu, An identity relating a theta series to a sum of Lambert series, Bull. London Math. Soc., 33 (2001), 25-31.
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p 102 eq 9.
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FORMULA
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Coefficients in expansion of Sum_{ i, j = -inf .. inf } q^(i^2+7*j^2).
Euler transform of period 28 sequence [2, -3, 2, -1, 2, -3, 4, -1, 2, -3, 2, -1, 2, -6, 2, -1, 2, -3, 2, -1, 4, -3, 2, -1, 2, -3, 2, -2, ...].
Expansion of (eta(q^2)eta(q^14))^5/(eta(q)eta(q^4)eta(q^7)eta(q^28))^2 in powers of q.
G.f.: theta_3(q)theta_3(q^7) = Product_{k>0} (1-q^(2k))(1+q^(2k-1))^2(1-q^(14k))(1+q^(14k-7))^2.
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PROGRAM
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(PARI) a(n)=local(X); if(n<0, 0, X=x+x*O(x^n); polcoeff(eta(X)^-2*eta(X^2)^5*eta(X^4)^-2*eta(X^7)^-2*eta(X^14)^5*eta(X^28)^-2, n))
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CROSSREFS
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Sequence in context: A079807 A116373 A096142 this_sequence A024164 A138805 A061897
Adjacent sequences: A033716 A033717 A033718 this_sequence A033720 A033721 A033722
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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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