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A163525 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I. 1
1, 25, 600, 14400, 345600, 8294100, 199051200, 4777056300, 114645211200, 2751385708800, 66030872460900, 1584683711924400, 38031035684483100, 912711895976984400, 21904294481198985600, 525684083700365474100 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170744, 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..720

Index entries for linear recurrences with constant coefficients, signature (23, 23, 23, 23, -276).

FORMULA

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(276*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).

MATHEMATICA

CoefficientList[Series[(1+x)*(1-x^5)/(1-24*x+299*x^5-276*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)

coxG[{5, 276, -23}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 16 2019 *)

PROG

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-24*x+299*x^5-276*x^6)) \\ G. C. Greubel, Jul 27 2017

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-24*x+299*x^5-276*x^6) )); // G. C. Greubel, May 16 2019

(Sage) ((1+x)*(1-x^5)/(1-24*x+299*x^5-276*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019

CROSSREFS

Sequence in context: A104643 A162811 A163175 * A163993 A164638 A164963

Adjacent sequences:  A163522 A163523 A163524 * A163526 A163527 A163528

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified October 17 22:42 EDT 2019. Contains 328134 sequences. (Running on oeis4.)