A266769 -id:A266769 - cp's OEIS frontend

A282044 Reduced Kronecker coefficients for the case a=2, b=3, i=4.

0, 0, 0, 0, 1, 2, 5, 9, 16, 24, 37, 51, 71, 93

Offset: 0

N. J. A. Sloane, Feb 21 2017

Table 3 of Colmenarejo (2016) shows this sequence as the missing member of the family A266769, A000601, A006918, A014126, A282044, A175287.

It would be nice to have a g.f.

Laura Colmenarejo, Combinatorics on several families of Kronecker coefficients related to plane partitions, arXiv:1604.00803 [math.CO], 2016.

Cf. A266769, A000601, A006918, A014126, A175287.

Conjectured g.f.: x^4*(1+x^2)/(1-2*x+x^3+3*x^5-4*x^6). - Jean-François Alcover, Feb 18 2019.

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

Original entry on oeis.org

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

N. J. A. Sloane, Jan 10 2016

nonn

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.

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

Index entries for Molien series

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

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 *)

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.

cp's OEIS Frontend

A282044 Reduced Kronecker coefficients for the case a=2, b=3, i=4.

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