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A166128 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I. 1
1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513198112, 846067909140976, 26228105183354880, 813071260683525120, 25205209081174517760, 781361481515952460800, 24222205926980341002240 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170751, 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 (30, 30, 30, 30, 30, 30, 30, 30, 30, -465).

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)/(465*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).

MAPLE

seq(coeff(series((1+t)*(1-t^10)/(1 -31*t +495*t^10 -465*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 -31*t +495*t^10 -465*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 26 2016 *)

coxG[{465, 10, -30}] (* The coxG program is at A169452 *) (* G. C. Greubel, Mar 11 2020 *)

PROG

(Sage)

def A166128_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

return P( (1+t)*(1-t^10)/(1 -31*t +495*t^10 -465*t^11) ).list() A166128_list(30) # G. C. Greubel, Mar 11 2020

CROSSREFS

Sequence in context: A164668 A165131 A165548 * A166426 A166622 A167085

Adjacent sequences:  A166125 A166126 A166127 * A166129 A166130 A166131

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified May 31 06:45 EDT 2020. Contains 334747 sequences. (Running on oeis4.)