A092497 Molien series for 16-dimensional group of structure Z_2^4.S_3 and order 96, corresponding to complete weight enumerators of Hermitian self-dual GF(4)-linear codes over GF(16) containing the all-ones vector.

1, 1, 5, 16, 64, 196, 661, 1921, 5431, 14106, 35006, 81858, 183616, 393568, 813916, 1624114, 3143974, 5910904, 10831414, 19369614, 33887006, 58069748, 97645340, 161289668, 262066349, 419245385, 661069025, 1028234130, 1578996010, 2395570650, 3593235173

Offset

0,3

Links

Table of n, a(n) for n=0..30.

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006. See Section 7.6.1, especially Eq. (7.6.16), p. 220.

Index entries for Molien series

Formula

For the Molien series see the Maple code.

Maple

f1:= 1 + 4*t^3 + 34*t^4 + 88*t^5 + 237*t^6 + 516*t^7 + 1161*t^8 + 2176*t^9 + 3726*t^10 + 5478*t^11 + 7524*t^12 + 9296*t^13 + 10805*t^14 + 5610 *t^15;
f2:=expand(t^30*subs(t=1/t, f1));
g:= (1-t)*(1-t^2)^4*(1-t^3)^7*(1-t^4)^4;
h:=(f1+f2)/g; # This is the Molien series
series(h, t, 48); # N. J. A. Sloane, Jan 29 2021

Crossrefs

Cf. A092496.

Sequence in context: A197549 A365907 A034532 * A275100 A301958 A349568

Adjacent sequences: A092494 A092495 A092496 * A092498 A092499 A092500

Keyword

nonn

Author

N. J. A. Sloane, Apr 05 2004

Extensions

There were errors in the definition (in the order and structure of the group). The Molien series was correct, but to make it easier to check I replaced the formulas with Maple code. Thanks to Georg Fischer and Andrey Zabolotskiy for noticing that something was wrong. - N. J. A. Sloane, Jan 29 2021

Status

approved