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A163749 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I. 1
1, 45, 1980, 87120, 3833280, 168663330, 7421142960, 326528374590, 14367164193360, 632151515809440, 27814503513864870, 1223830974655177020, 53848246968666559530, 2369308966391783748420, 104248982914726676312880 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170764, 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..605

Index entries for linear recurrences with constant coefficients, signature (43,43,43,43,-946).

FORMULA

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(946*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).

a(n) = 43*a(n-1)+43*a(n-2)+43*a(n-3)+43*a(n-4)-946*a(n-5). - Wesley Ivan Hurt, May 11 2021

MAPLE

seq(coeff(series((1+t)*(1-t^5)/(1-44*t+989*t^5-946*t^6), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Aug 09 2019

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^5)/(1-44*t+989*t^5-946*t^6), {t, 0, 20}], t] (* G. C. Greubel, Aug 02 2017 *)

coxG[{5, 946, -43}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 09 2019 *)

PROG

(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^5)/(1-44*t+989*t^5-946*t^6)) \\ G. C. Greubel, Aug 02 2017

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-43*t+945*t^5-903*t^6) )); // G. C. Greubel, Aug 09 2019

(Sage)

def A163749_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^5)/(1-43*t+945*t^5-903*t^6)).list()

A163749_list(20) # G. C. Greubel, Aug 09 2019

(GAP) a:=[45, 1980, 87120, 3833280, 168663330];; for n in [6..30] do a[n]:=43*(a[n-1]+a[n-2]+a[n-3]+a[n-4]) -946*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, Aug 09 2019

CROSSREFS

Sequence in context: A318221 A162885 A163231 * A164330 A164690 A165177

Adjacent sequences:  A163746 A163747 A163748 * A163750 A163751 A163752

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified July 24 05:05 EDT 2021. Contains 346273 sequences. (Running on oeis4.)