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

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			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 + ...
		

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.

Programs

Magma

L:=Lattice("A",5); T1 := ThetaSeries(L,120);

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 *)

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