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A163802 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I. 1
1, 46, 2070, 93150, 4191750, 188627715, 8488200600, 381966932160, 17188417679400, 773474553522000, 34806164017265190, 1566268790718951000, 70481709031863535560, 3171659511757241439000, 142723895272921025613000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170765, 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..600

Index entries for linear recurrences with constant coefficients, signature (44,44,44,44,-990).

FORMULA

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(990*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1).

a(n) = 44*a(n-1)+44*a(n-2)+44*a(n-3)+44*a(n-4)-990*a(n-5). - Wesley Ivan Hurt, May 11 2021

MAPLE

seq(coeff(series((1+t)*(1-t^5)/(1-45*t+1034*t^5-990*t^6), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Aug 09 2019

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^5)/(1-45*t+1034*t^5-990*t^6), {t, 0, 20}], t] (* G. C. Greubel, Aug 04 2017 *)

coxG[{5, 990, -44}] (* 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)/(1-45*t+1034*t^5-990*t^6)) \\ G. C. Greubel, Aug 04 2017

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-45*t+1034*t^5-990*t^6) )); // G. C. Greubel, Aug 09 2019

(Sage)

def A163802_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^5)/(1-45*t+1034*t^5-990*t^6)).list()

A163802_list(20) # G. C. Greubel, Aug 09 2019

(GAP) a:=[46, 2070, 93150, 4191750, 188627715];; for n in [6..30] do a[n]:=44*(a[n-1]+a[n-2]+a[n-3]+a[n-4]) -990*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, Aug 09 2019

CROSSREFS

Sequence in context: A324451 A162889 A163232 * A164331 A164691 A165178

Adjacent sequences:  A163799 A163800 A163801 * A163803 A163804 A163805

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified January 22 01:28 EST 2022. Contains 350481 sequences. (Running on oeis4.)