A051354 Expansion of Molien series for 16-dimensional complex Clifford group of genus 4 and order 97029351014400.

1, 1, 2, 7, 19, 52, 172, 550, 1782, 5845, 18508, 56345, 164157, 454518, 1196924, 3003750, 7198311, 16523847, 36447873, 77478005, 159172517, 316874035, 612729396, 1153359711, 2117566545, 3798941401, 6670327291, 11479693332, 19390588953, 32185179449, 52553840336

Offset

0,3

Comments

Oura gives an explicit formula for the Molien series that produces A027672; the present sequence is the subsequence formed from the terms whose exponents are multiples of 8 (that is, every other term of A027672). In other words, the present Molien series is (f(x)+f(z*x))/2, where z = exp(2*Pi*I/8) and f(x) is the Molien series for the group H_4 given explicitly by Oura in Theorem 4.1.

Links

Ray Chandler, Table of n, a(n) for n = 0..1000

Ray Chandler, Mathematica program

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

M. Oura, The dimension formula for the ring of code polynomials in genus 4, Osaka J. Math. 34 (1997), 53-72.

Index entries for linear recurrences with constant coefficients, signature (3, -2, 0, -3, 5, -2, -1, -1, 8, -7, -2, 2, 7, -7, -3, 1, 9, -11, 4, 3, 5, -9, -1, 0, 13, -15, 0, 4, 6, -9, 0, 8, 9, -18, -2, 12, -4, -4, -3, 6, 6, -8, -7, 18, -1, -6, -13, 13, 6, -14, -10, 30, -10, -10, -4, 22, -5, -6, -15, 28, -15, -6, -5, 22, -4, -10, -10, 30, -10, -14, 6, 13, -13, -6, -1, 18, -7, -8, 6, 6, -3, -4, -4, 12, -2, -18, 9, 8, 0, -9, 6, 4, 0, -15, 13, 0, -1, -9, 5, 3, 4, -11, 9, 1, -3, -7, 7, 2, -2, -7, 8, -1, -1, -2, 5, -3, 0, -2, 3, -1).

Index entries for Molien series

Formula

a(n) = A027672(2*n).

Example

1 + t^8 + 2*t^16 + 7*t^24 + 19*t^32 + 52*t^40 + 172*t^48 + ...

Mathematica

See link for Mathematica program.

Crossrefs

Cf. A027672, A003956, A008621, A008718, A024186, A008620, A028288, A043330.

Sequence in context: A328990 A099484 A018030 * A073799 A040016 A145519

Adjacent sequences: A051351 A051352 A051353 * A051355 A051356 A051357

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

Edited by Georg Fischer, Jan 24 2021

Status

approved