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A163669 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I. 1
1, 40, 1560, 60840, 2372760, 92536860, 3608907120, 140746192080, 5489055252720, 214071351558480, 8348712382781940, 325597040159662440, 12698177599143380760, 495224754685478312040, 19313602738540732379160 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170759, 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..625

Index entries for linear recurrences with constant coefficients, signature (38, 38, 38, 38, -741).

FORMULA

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(741*t^5 - 38*t^4 - 38*t^3 - 38*t^2 - 38*t + 1).

MATHEMATICA

CoefficientList[Series[(1+x)*(1-x^5)/(1-39*x+779*x^5-741*x^6), {x, 0, 20}], x] (* G. C. Greubel, Aug 01 2017 *)

coxG[{5, 741, -38}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 23 2019 *)

PROG

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-39*x+779*x^5-741*x^6)) \\ G. C. Greubel, Aug 01 2017

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-39*x+779*x^5-741*x^6) )); // G. C. Greubel, May 23 2019

(Sage) ((1+x)*(1-x^5)/(1-39*x+779*x^5-741*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 23 2019

(GAP) a:=[40, 1560, 60840, 2372760, 92536860];; for n in [6..20] do a[n]:=38*(a[n-1]+a[n-2] +a[n-3]+a[n-4]) -741*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, May 23 2019

CROSSREFS

Sequence in context: A165371 A162877 A163223 * A164085 A164684 A165172

Adjacent sequences:  A163666 A163667 A163668 * A163670 A163671 A163672

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified July 4 08:33 EDT 2020. Contains 335444 sequences. (Running on oeis4.)