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A166225 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I. 1
1, 41, 1640, 65600, 2624000, 104960000, 4198400000, 167936000000, 6717440000000, 268697600000000, 10747903999999180, 429916159999934400, 17196646399996064820, 687865855999790145600, 27514634239989507936000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170760, 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 (39, 39, 39, 39, 39, 39, 39, 39, 39, -780).

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)/(780*t^10 - 39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).

MAPLE

seq(coeff(series((1+t)*(1-t^10)/(1-40*t+819*t^10-780*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^10)/(1-40*t+819*t^10-780*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 07 2016 *)

coxG[{10, 780, -39}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 30 2018 *)

PROG

(Sage)

def A166225_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P( (1+t)*(1-t^10)/(1-40*t+819*t^10-780*t^11) ).list()

A166225_list(30) # G. C. Greubel, Mar 11 2020

CROSSREFS

Sequence in context: A164685 A165173 A165692 * A166435 A166714 A167094

Adjacent sequences:  A166222 A166223 A166224 * A166226 A166227 A166228

KEYWORD

nonn

AUTHOR

John Cannon and N. J. A. Sloane, Dec 03 2009

STATUS

approved

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Last modified August 9 06:47 EDT 2022. Contains 356018 sequences. (Running on oeis4.)