A029751 Average theta series of odd unimodular lattices in dimension 12.

1, 8, 248, 1952, 7928, 25008, 60512, 134464, 253688, 474344, 775248, 1288416, 1934432, 2970352, 4168384, 6101952, 8118008, 11358864, 14704664, 19808800, 24782928, 32809216, 39940896, 51490752, 61899872, 78150008, 92080912, 115265600, 133253824, 164089200, 189160512

Offset

0,2

References

E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, NY, 1985, p. 121.

R. A. Rankin, Modular Forms, p. 240 ff.

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Formula

G.f.: 1 + 8*Sum_{k>0} k^5 * x^k / (1+x^k). - Michael Somos, Sep 21 2005 [corrected by Sean A. Irvine, Apr 14 2026]

A000145(2*n + 1) = a(2*n + 1) + 16*A000735(n). - Michael Somos, Sep 21 2005 [corrected by Daniel Suteu, Apr 14 2026]

a(2*n + 1) = 8*sigma_5(2*n + 1). - Daniel Suteu, Apr 14 2026

Mathematica

a[0] = 1; a[n_] := (-1)^(n-1)*8*DivisorSum[n, (-1)^(n + n/#)*#^5&]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jul 06 2017, translated from PARI *)

Prog

(PARI) a(n)=if(n<1, n==0, (-1)^(n-1)*8*sumdiv(n, d, (-1)^(n+n/d)*d^5)) /* Michael Somos, Sep 21 2005 */

Crossrefs

Cf. A000145, A000735.

Sequence in context: A316802 A299648 A219269 * A035036 A221518 A317519

Adjacent sequences: A029748 A029749 A029750 * A029752 A029753 A029754

Keyword

nonn

Author

N. J. A. Sloane

Status

approved