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A144060 Expansion of Molien series for the ring of genus 5 code polynomials for Type II codes.

%I A144060 #26 Aug 08 2025 03:54:01
%S A144060 1,0,1,0,2,2,8,8,34,60,203,553,2063,7359,30811,127416,541644,2235677,
%T A144060 8966371,34413747,126465849,443858877,1490702752,4796609651,
%U A144060 14821521743,44071296447,126388352322,350298687803,940211047828,2448320130626,6196158876181
%N A144060 Expansion of Molien series for the ring of genus 5 code polynomials for Type II codes.
%H A144060 Ray Chandler, <a href="/A144060/b144060.txt">Table of n, a(n) for n = 0..2000</a>
%H A144060 Ray Chandler, <a href="/A144060/a144060.txt">Mathematica program</a>
%H A144060 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 A144060 M. Oura, <a href="http://projecteuclid.org/euclid.ojm/1200787332">The dimension formula for the ring of code polynomials in genus 4</a>, Osaka J. Math. 34 (1997), 53-72.
%H A144060 M. Oura, <a href="http://web.archive.org/web/20070102035724/http://www.math.kochi-u.ac.jp/oura/molienH5">The dimension formula of the invariant ring of H5</a> (web archive).
%H A144060 <a href="/index/Rec#order_532">Index entries for linear recurrences with constant coefficients</a>, order 532.
%F A144060 Oura (see link) gives the Molien series explicitly.
%e A144060 1 + x^8 + 2*x^16 + 2*x^20 + 8*x^24 + 8*x^28 + 34*x^32 + 60*x^36 + 203*x^40 + 553*x^44 + 2063*x^48 + 7359*x^52 + 30811*x^56 + 127416*x^60 + 541644*x^64 + 2235677*x^68 + 8966371*x^72 + 34413747*x^76 + 126465849*x^80 + 443858877*x^84 + 1490702752*x^88 + 4796609651*x^92 + 14821521743*x^96 + .....
%t A144060 (* See link for Mathematica program. *)
%Y A144060 Cf. A027672, A051354.
%K A144060 nonn
%O A144060 0,5
%A A144060 _N. J. A. Sloane_, Dec 22 2008, following a suggestion from G. Nebe
%E A144060 More terms from _Ray Chandler_, Mar 23 2017