A166365 - OEIS

A166365

Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 7, 42, 252, 1512, 9072, 54432, 326592, 1959552, 11757312, 70543872, 423263211, 2539579140, 15237474105, 91424840220, 548549014860, 3291293930400, 19747762629840, 118486570063680, 710919386089920, 4265516110786560

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OFFSET

0,2

COMMENTS

The initial terms coincide with those of A003949, 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 (5,5,5,5,5,5,5,5,5,5,-15).

FORMULA

G.f.: (t^11 + 2*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)/(15*t^11 - 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).

MAPLE

seq(coeff(series((1+t)*(1-t^11)/(1-6*t+20*t^11-15*t^12), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 13 2020

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^11)/(1-6*t+20*t^11-15*t^12), {t, 0, 30}], t] (* G. C. Greubel, May 10 2016 *)

coxG[{11, 15, -5}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 13 2020 *)

PROG

(Sage)

def A166365_list(prec):

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

return P( (1+t)*(1-t^11)/(1-6*t+20*t^11-15*t^12) ).list()

A166365_list(30) # G. C. Greubel, Aug 10 2019

CROSSREFS