A097913 - OEIS

%I #16 Mar 21 2023 09:40:21

%S 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,

%T 12,15,15,16,16,19,19,20,20,23,23,26,26,29,29,30,30,36,36,39,39,42,42,

%U 45,45,51,51,54,54,60,60,63,63,69,69,75,75,81,81,84,84,94,94,100,100,106,106

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

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

%H G. C. Greubel, <a href="/A097913/b097913.txt">Table of n, a(n) for n = 0..1000</a>

%H G. Nebe, E. M. Rains and N. J. A. Sloane, <a href="http://neilsloane.com/doc/cliff2.html">Self-Dual Codes and Invariant Theory</a>, Springer, Berlin, 2006.

%H <a href="/index/Rec#order_45">Index entries for linear recurrences with constant coefficients</a>, 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).

%t 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 *)

%o (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

%Y Cf. A008718.

%K nonn

%O 0,9

%A _N. J. A. Sloane_, Sep 04 2004