A002520 Theta series of 28-dimensional unimodular lattice with no roots and with no parity vector of norm 4.

1, 0, 0, 2240, 98280, 1790208, 19138560, 141920640, 805208040, 3723722240, 14651449344, 50573436480, 156717687840, 443691198720, 1162883174400, 2851049534592, 6596666916840, 14509544394240, 30507984568320

Offset

0,4

Links

Table of n, a(n) for n=0..18.

R. Bacher and B. B. Venkov, Réseaux entiers unimodulaires sans racine en dimension 27 et 28, in Réseaux euclidiens, designs sphériques et formes modulaires, pp. 212-267, Enseignement Math., Geneva, 2001.

Formula

t3^28-56*t3^20*D8+280*t3^12*D8^2 where t3=theta_3(z) and D8=(theta_2(z)*theta_4(z))^4/16.

Mathematica

terms = 19; t3[z_] := EllipticTheta[3, 0, z]; D8[z_] := (EllipticTheta[2, 0, z]*EllipticTheta[4, 0, z])^4/16; s = t3[z]^28 - 56*t3[z]^20*D8[z] + 280*t3[z]^12*D8[z]^2 + O[z]^terms; CoefficientList[s, z] (* Jean-François Alcover, Jul 05 2017 *)

Crossrefs

Cf. A002519.

Sequence in context: A079013 A186865 A038728 * A337416 A183771 A271470

Adjacent sequences: A002517 A002518 A002519 * A002521 A002522 A002523

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Extensions

More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 04 2000

Status

approved