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A163745 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I. 1
1, 43, 1806, 75852, 3185784, 133802025, 5619647124, 236023587219, 9912923799660, 416339991317124, 17486161688852682, 734413837213650321, 30845173108213815708, 1295488532304021561975, 54410151353124129064362 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170762, 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..614

Index entries for linear recurrences with constant coefficients, signature (41, 41, 41, 41, -861).

FORMULA

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(861*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).

a(n) = 41*a(n-1)+41*a(n-2)+41*a(n-3)+41*a(n-4)-861*a(n-5). - Wesley Ivan Hurt, May 11 2021

MAPLE

seq(coeff(series((1+t)*(1-t^5)/(1-42*t+902*t^5-861*t^6), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Aug 09 2019

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^5)/(1-42*t+902*t^5-861*t^6), {t, 0, 20}], t] (* G. C. Greubel, Aug 02 2017 *)

coxG[{5, 865, -41}] (* 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)/(1-42*t+902*t^5-861*t^6)) \\ G. C. Greubel, Aug 02 2017

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-42*t+902*t^5-861*t^6) )); // G. C. Greubel, Aug 09 2019

(Sage)

def A163745_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^5)/(1-42*t+902*t^5-861*t^6)).list()

A163745_list(20) # G. C. Greubel, Aug 09 2019

CROSSREFS

Sequence in context: A198206 A162881 A163226 * A164113 A164687 A165175

Adjacent sequences:  A163742 A163743 A163744 * A163746 A163747 A163748

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified August 4 09:50 EDT 2021. Contains 346446 sequences. (Running on oeis4.)