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A163404 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I. 1
1, 11, 110, 1100, 11000, 109945, 1098900, 10983555, 109781100, 1097266500, 10967222970, 109617836625, 1095634704780, 10950913128375, 109454819042250, 1094005337374620, 10934627535602100, 109292043884611005 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A003953, 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..995

Index entries for linear recurrences with constant coefficients, signature (9, 9, 9, 9, -45).

FORMULA

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(45*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).

MATHEMATICA

CoefficientList[Series[(1 + x)*(1-x^5)/(1-10*x+54*x^5-45*x^6), {x, 0, 30}], x] (* or *)  LinearRecurrence[{9, 9, 9, 9, -45}, {1, 11, 110, 1100, 11000, 109945}, 30]] (* G. C. Greubel, Dec 21 2016 *)

coxG[{5, 45, -9}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 12 2019 *)

PROG

(PARI) my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-10*x+54*x^5-45*x^6)) \\ G. C. Greubel, Dec 21 2016

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-10*x+54*x^5-45*x^6) )); // G. C. Greubel, May 12 2019

(Sage) ((1+x)*(1-x^5)/(1-10*x+54*x^5-45*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019

CROSSREFS

Sequence in context: A121031 A115804 A162987 * A115808 A163955 A164590

Adjacent sequences:  A163401 A163402 A163403 * A163405 A163406 A163407

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified August 18 08:57 EDT 2019. Contains 326077 sequences. (Running on oeis4.)