A008445 Theta series of A_5 lattice.

1, 30, 90, 140, 270, 360, 330, 660, 810, 570, 1020, 1260, 1100, 1560, 1620, 1452, 2190, 2340, 1710, 2940, 3240, 1920, 3360, 3960, 2970, 3930, 4140, 3920, 5460, 4680, 3360, 5940, 6570, 4620, 6180, 7560, 5130, 7320, 7920, 5280, 9180, 8100, 6600, 10500, 9900

Offset

0,2

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 110.

Links

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

LMFDB, Integral Lattice A5.

Example

1 + 30*q^2 + 90*q^4 + 140*q^6 + 270*q^8 + 360*q^10 + 330*q^12 + 660*q^14 + 810*q^16 + 570*q^18 + 1020*q^20 + 1260*q^22 + 1100*q^24 + 1560*q^26 + 1620*q^28 + 1452*q^30 + 2190*q^32 + 2340*q^34 + 1710*q^36 + 2940*q^38 + 3240*q^40 + 1920*q^42 + 3360*q^44 + 3960*q^46 + 2970*q^48 + ...

Mathematica

terms = 45; f[q_] = LatticeData["A5", "ThetaSeriesFunction"][-I Log[q]/Pi]; s = Series[f[q], {q, 0, 2 terms}]; CoefficientList[s, q^2][[1 ;; terms]] (* Jean-François Alcover, Jul 04 2017 *)

Prog

(Magma) L:=Lattice("A", 5); T1<q> := ThetaSeries(L, 120);
(PARI)
seq(N) = {
  my(q=[2, -1, 0, 0, 0; -1, 2, -1, 0, 0; 0, -1, 2, -1, 0;
        0, 0, -1, 2, -1; 0, 0, 0, -1, 2]);
  concat(1, 2*Vec(qfrep(q, N-1, 1)));
};
seq(45) \\ Gheorghe Coserea, Nov 25 2018

Crossrefs

Sequence in context: A126384 A025417 A081807 * A039462 A370495 A138018

Adjacent sequences: A008442 A008443 A008444 * A008446 A008447 A008448

Keyword

nonn

Author

N. J. A. Sloane

Status

approved