A045867 Theta series of quadratic form with Gram matrix [ 4, 1, 2, 1; 1, 4, 1, 0; 2, 1, 6, -2; 1, 0, -2, 20 ].

1, 0, 4, 6, 2, 6, 2, 6, 10, 2, 8, 14, 24, 10, 14, 10, 26, 14, 38, 14, 32, 18, 14, 16, 40, 20, 24, 34, 40, 12, 60, 24, 34, 18, 36, 30, 50, 2, 40, 30, 60, 34, 70, 30, 64, 64, 52, 42, 72, 42, 60, 50, 72, 34, 62, 38, 80, 54, 72, 36, 100, 52, 56, 76, 90, 52, 126, 36, 80, 72, 100

Offset

0,3

Comments

This is the 4-dimensional Elkies_C lattice.

Links

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

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

Example

G.f. = 1 + 4*x^2 + 6*x^3 + 2*x^4 + 6*x^5 + 2*x^6 + 6*x^7 + 10*x^8 + 2*x^9 + ...
G.f. = 1 + 4*q^4 + 6*q^6 + 2*q^8 + 6*q^10 + 2*q^12 + 6*q^14 + 10*q^16 + ...

Prog

(PARI) {a(n) = my(G); if( n<0, 0, G = [ 4, 1, 2, 1; 1, 4, 1, 0; 2, 1, 6, -2; 1, 0, -2, 20]; polcoeff( 1 + 2 * x * Ser( qfrep( G, n, 1)), n))}; /* Michael Somos, Apr 02 2006 */
(Magma) A := Basis( ModularForms( Gamma0(37), 2), 71); A[1] + 4*A[3]; /* Michael Somos, Mar 30 2015 */

Crossrefs

Dual lattice to A045866.

Sequence in context: A010669 A225092 A029677 * A236189 A347910 A342875

Adjacent sequences: A045864 A045865 A045866 * A045868 A045869 A045870

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved