A045865 Theta series of quadratic form with Gram matrix [ 4, 0, 2, 1; 0, 2, 1, 1; 2, 1, 20, 1; 1, 1, 1, 10 ].

1, 2, 2, 4, 2, 4, 8, 4, 10, 6, 12, 12, 16, 4, 16, 16, 26, 20, 26, 16, 28, 20, 24, 24, 40, 14, 28, 20, 40, 12, 48, 16, 42, 36, 36, 32, 66, 2, 40, 32, 60, 16, 64, 40, 48, 52, 48, 36, 88, 30, 62, 56, 76, 32, 80, 48, 80, 56, 60, 56, 112, 52, 64, 72, 74, 56, 96, 40, 68, 72, 96, 28

Offset

0,2

Comments

This is the 4-dimensional Elkies_A lattice.

References

N. D. Elkies, Elliptic and modular curves..., in AMS/IP Studies in Advanced Math., 7 (1998), 21-76, esp. p. 57.

Links

John Cannon, Table of n, a(n) for n = 0..5000

Example

G.f. = 1 + 2*x + 2*x^2 + 4*x^3 + 2*x^4 + 4*x^5 + 8*x^6 + 4*x^7 + 10*x^8 + ...
G.f. = 1 + 2*q^2 + 2*q^4 + 4*q^6 + 2*q^8 + 4*q^10 + 8*q^12 + 4*q^14 + 10*q^16 + 6*q^18 + ...

Prog

(PARI)  {a(n) = my(G); if( n<0, 0, G = [ 4, 0, 2, 1; 0, 2, 1, 1; 2, 1, 20, 1; 1, 1, 1, 10 ]; polcoeff( 1 + 2 * x * Ser( qfrep( G, n, 1)), n))}; /* Michael Somos, Mar 30 2015 */
(Magma) A := Basis( ModularForms( Gamma0(37), 2), 72); A[1] + 2*A[2] + 2*A[3]; /* Michael Somos, Mar 30 2015 */

Crossrefs

Sequence in context: A183402 A217839 A083779 * A319862 A220977 A054134

Adjacent sequences: A045862 A045863 A045864 * A045866 A045867 A045868

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 22 2000

Status

approved