A097913 G.f.: (1+x^18)/((1-x)*(1-x^8)*(1-x^12)*(1-x^24)).

1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 6, 9, 9, 10, 10, 11, 11, 12, 12, 15, 15, 16, 16, 19, 19, 20, 20, 23, 23, 26, 26, 29, 29, 30, 30, 36, 36, 39, 39, 42, 42, 45, 45, 51, 51, 54, 54, 60, 60, 63, 63, 69, 69, 75, 75, 81, 81, 84, 84, 94, 94, 100, 100, 106, 106

Offset: 0

Author

N. J. A. Sloane, Sep 04 2004

Keywords

• nonn

Comments

Conjectured Poincaré series [or Poincare series] for genus 2 Siegel theta series of odd unimodular lattices.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
• Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1).

Crossrefs

Cf. A008718.

Programs

Mathematica

CoefficientList[Series[(1 + x^18)/((1 - x)*(1 - x^8)*(1 - x^12)*(1 - x^24)), {x, 0, 50}], x] (* G. C. Greubel, Dec 20 2017 *)

PARI

x='x+O('x^30); Vec((1+x^18)/((1-x)*(1-x^8)*(1-x^12)*(1-x^24))) \\ G. C. Greubel, Dec 20 2017