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A046113
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Coefficients in expansion of theta_3(q) * theta_3(q^6) in powers of q.
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1
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1, 2, 0, 0, 2, 0, 2, 4, 0, 2, 4, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 4, 0, 2, 6, 0, 0, 4, 0, 0, 4, 0, 4, 0, 0, 2, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 2, 8, 0, 0, 4, 0, 4, 0, 0, 4, 2, 0, 0, 0, 0, 0, 8, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Number of representations of n as a sum of six times a square and a square. - Ralf Stephan, May 14 2007
a(n) < 2 if and only if n is in A002480. a(n) > 0 if and only if n is in A002481. - Michael Somos Mar 01 2011
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REFERENCES
| J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p 102 eq 9.
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LINKS
| A. Berkovich and H. Yesilyurt, Ramanujan's identities and representation of integers by certain binary and quaternary quadratic forms
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FORMULA
| G.f.: Sum_{ i, j = -inf .. inf } q^(i^2 + 6*j^2).
a(n) = A000377(n) + A115660(n). - Michael Somos Mar 01 2011
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EXAMPLE
| 1 + 2*x + 2*x^4 + 2*x^6 + 4*x^7 + 2*x^9 + 4*x^10 + 4*x^15 + 2*x^16 + ...
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PROG
| (PARI) {a(n) = if( n<0, 0, polcoeff( 1 + 2 * x * Ser( qfrep([ 1, 0; 0, 6], n)), n))} /* Michael Somos Mar 01 2011 */
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CROSSREFS
| Cf. A000377, A002480, A002481, A115660.
Sequence in context: A110036 A086937 A095759 * A143068 A028959 A079181
Adjacent sequences: A046110 A046111 A046112 * A046114 A046115 A046116
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 18 2002
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