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A046113 Coefficients in expansion of theta_3(q) * theta_3(q^6) in powers of q. 5
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; text; internal format)
OFFSET

0,2

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

REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p 102 eq 9.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000

A. Berkovich and H. Yesilyurt, Ramanujan's identities and representation of integers by certain binary and quaternary quadratic forms

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

EXAMPLE

G.f. = 1 + 2*x + 2*x^4 + 2*x^6 + 4*x^7 + 2*x^9 + 4*x^10 + 4*x^15 + 2*x^16 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q] EllipticTheta[ 3, 0, q^6], {q, 0, n}]; (* Michael Somos, Apr 19 2015 *)

PROG

(PARI) {a(n) = my(G); if( n<0, 0, G = [ 1, 0; 0, 6]; polcoeff( 1 + 2 * x * Ser( qfrep( G, n)), n))}; /* Michael Somos, Mar 01 2011 */

CROSSREFS

Cf. A000377, A002480, A002481, A115660.

Sequence in context: A291289 A095759 A260309 * A262938 A143068 A261202

Adjacent sequences:  A046110 A046111 A046112 * A046114 A046115 A046116

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 18 2002

STATUS

approved

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Last modified November 12 19:19 EST 2018. Contains 317116 sequences. (Running on oeis4.)