A166130 - OEIS

A166130

Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 34, 1122, 37026, 1221858, 40321314, 1330603362, 43909910946, 1449027061218, 47817893020194, 1577990469665841, 52073685498954240, 1718431621464879552, 56708243508320883072, 1871372035773924450624, 61755277180517572075776

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OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170753, although the two sequences are eventually different.

Computed with Magma using commands similar to those used to compute A154638.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (32,32,32,32,32,32,32,32,32,-528).

FORMULA

G.f.: (t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(528*t^10 - 32*t^9 - 32*t^8 - 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).

MAPLE

seq(coeff(series((1+t)*(1-t^10)/(1-33*t+560*t^10-528*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^10)/(1-33*t+560*t^10-528*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 26 2016 *)

coxG[{528, 10, -32}] (* The coxG program is at A169452 *) (* G. C. Greubel, Mar 11 2020 *)

PROG

(SageMath)

def A166130_list(prec):

P.<t> = PowerSeriesRing(ZZ, prec)

return P( (1+t)*(1-t^10)/(1-33*t+560*t^10-528*t^11) ).list()

A166130_list(30) # G. C. Greubel, Mar 11 2020

CROSSREFS