A266771 Molien series for invariants of finite Coxeter group D_8 (bisected).

1, 1, 2, 3, 6, 8, 13, 18, 27, 36, 51, 67, 92, 118, 156, 198, 256, 319, 404, 498, 620, 755, 926, 1116, 1353, 1615, 1935, 2291, 2720, 3194, 3759, 4384, 5120, 5932, 6879, 7923, 9131, 10458, 11981, 13654, 15561, 17648, 20014, 22600, 25514, 28692, 32255, 36134, 40464, 45167

Offset

0,3

Comments

The Molien series for the finite Coxeter group of type D_k (k >= 3) has G.f. = 1/Prod_i (1-x^(1+m_i)) where the m_i are [1,3,5,...,2k-3,k-1]. If k is even only even powers of x appear, and we bisect the sequence.

References

J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.1, page 59.

Links

Table of n, a(n) for n=0..49.

Index entries for Molien series

Formula

G.f.: 1/((1-t^8)^2*(1-t^2)*(1-t^4)*(1-t^6)*(1-t^10)*(1-t^12)*(1-t^14)), bisected.

Mathematica

Take[CoefficientList[Series[1/((1-x^8)Times@@(1-x^Range[2, 14, 2])), {x, 0, 100}], x], {1, -1, 2}] (* Harvey P. Dale, Jan 02 2018 *)

Crossrefs

Molien series for finite Coxeter groups D_3 through D_12 are A266755, A266769, A266768, A003402, and A266770-A266775.

Sequence in context: A239952 A353902 A240076 * A295342 A226635 A024788

Adjacent sequences: A266768 A266769 A266770 * A266772 A266773 A266774

Keyword

nonn

Author

N. J. A. Sloane, Jan 10 2016

Status

approved