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).
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
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
Edited by Georg Fischer, Jan 24 2021
STATUS
approved