A092203 Molien series for 16-dimensional group of structure 2^4.O_{4}^{+}(F_2) = 2^4.(S_3 X S_3).2 and order 1152, corresponding to genus 2 complete weight enumerators of Hermitian self-dual GF(2)-linear codes over GF(4) containing the all-ones vector.

1, 1, 3, 7, 21, 47, 128, 303, 754, 1735, 3989, 8712, 18687, 38482, 77421, 150813, 286925, 531306, 962637, 1704506, 2959412, 5037606, 8426351, 13854300, 22426944, 35759968, 56234440, 87258555, 133730542, 202529129, 303328391, 449478982, 659401717, 958118335, 1379571974, 1969206260

Offset

0,3

Links

Table of n, a(n) for n=0..35.

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006. See Section (7.6.1), and especially Eq. (7.6.14) on page 219.

Index entries for Molien series

Formula

For the Molien series see the Maple code.

Maple

f1:= 1 + t^3 + 5*t^4 + 18*t^5 + 45*t^6 + 88*t^7 + 196*t^8 + 394*t^9 + 804*t^10 + 1512*t^11 + 2702*t^12 + 4529*t^13 + 7218*t^14 + 11019*t^15 + 16064*t^16 + 22609*t ^17 + 30555*t^18 + 39889*t^19 + 50303*t^20 + 61476*t^21 + 72888*t^22 + 84047*t^23 + 94299*t^24 + 102995*t^25 + 109674*t^26 + 113791*t^27 + 57614*t^28;
f:= f1+expand(t^56*subs(t=1/t, f1));
g:= (1-t)*(1-t^2)^2*(1-t^3)^3*(1-t^4)^6*(1-t^6)*(1-t^8)^2*(1-t^12);
h:=f/g; # This is the Molien series
series(h, t, 48);

Crossrefs

Cf. A092201, A092497.

Sequence in context: A183936 A027151 A219589 * A018760 A050614 A181393

Adjacent sequences: A092200 A092201 A092202 * A092204 A092205 A092206

Keyword

nonn

Author

N. J. A. Sloane, Apr 02 2004

Extensions

There were errors in the definition (in the order and structure of the group). The rational form of the Molien series was correct, but the DATA section - the coefficients in the expansion of the Molien series - was wrong from the 28th term onwards. To make it easier to check I have replaced the formulas with Maple code based on the Latex source code for the book. Thanks to Georg Fischer and Andrey Zabolotskiy for noticing that something was wrong and proposing corrections. - N. J. A. Sloane, Jan 29 2021

Status

approved