login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Theta series of A_7 lattice.
5

%I #13 Sep 08 2022 08:44:35

%S 1,56,420,896,2366,3360,6440,7168,14196,14168,22120,24192,37912,33824,

%T 55440,50176,75838,71232,98700,88704,141960,117824,156520,150528,

%U 217672,173656,261240,218624,303424,273504,355600,301056,455028,359744,474320

%N Theta series of A_7 lattice.

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

%t terms = 29; f[q_] = LatticeData["A7", "ThetaSeriesFunction"][-I Log[q]/Pi]; s = Series[f[q], {q, 0, 2 terms}]; DeleteCases[CoefficientList[s, q^(1/2) ] // Round, 0][[1 ;; terms]] (* _Jean-François Alcover_, Jul 04 2017 *)

%o (Magma) L:=Lattice("A",7); T1<q> := ThetaSeries(L,60);

%Y Cf. A023919 (dual).

%K nonn

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Sean A. Irvine_, Jun 12 2019