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A163601 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I. 1
1, 36, 1260, 44100, 1543500, 54021870, 1890743400, 66175247880, 2316106686600, 81062789409000, 2837164567941270, 99299602743358500, 3475445596778953980, 121639178430430006500, 4257321634653990493500, 149004520868736130568670 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170755, 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..645

Index entries for linear recurrences with constant coefficients, signature (34, 34, 34, 34, -595).

FORMULA

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(595*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).

a(n) = 34*a(n-1)+34*a(n-2)+34*a(n-3)+34*a(n-4)-595*a(n-5). - Wesley Ivan Hurt, May 11 2021

MATHEMATICA

CoefficientList[Series[(1+x)*(1-x^5)/(1-35*x+629*x^5-595*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 29 2017 *)

coxG[{5, 595, -34}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 22 2019 *)

PROG

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-35*x+629*x^5-595*x^6)) \\ G. C. Greubel, Jul 29 2017

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-35*x+629*x^5-595*x^6) )); // G. C. Greubel, May 22 2019

(Sage) ((1+x)*(1-x^4)/(1-35*x+629*x^5-595*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 22 2019

(GAP) a:=[36, 1260, 44100, 1543500, 54021870];; for n in [6..20] do a[n]:=34*(a[n-1]+a[n-2] +a[n-3]+a[n-4]) - 595*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, May 22 2019

CROSSREFS

Sequence in context: A270961 A162850 A163219 * A164069 A164672 A165168

Adjacent sequences:  A163598 A163599 A163600 * A163602 A163603 A163604

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified August 15 02:47 EDT 2022. Contains 356122 sequences. (Running on oeis4.)