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A163878 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I. 1
1, 5, 20, 80, 320, 1280, 5110, 20400, 81450, 325200, 1298400, 5184000, 20697690, 82637820, 329940630, 1317324420, 5259563280, 20999387520, 83842374870, 334749945240, 1336526142210, 5336228292840, 21305481048360, 85064487085440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A003947, 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..1000

Index entries for linear recurrences with constant coefficients, signature (3,3,3,3,3,-6).

FORMULA

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(6*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1).

MAPLE

seq(coeff(series((1+t)*(1-t^6)/(1-4*t+9*t^6-6*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 10 2019

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^6)/(1-4*t+9*t^6-6*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 07 2017 *)

coxG[{6, 6, -3}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 10 2019 *)

PROG

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-4*t+9*t^6-6*t^7)) \\ G. C. Greubel, Aug 07 2017

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-4*t+9*t^6-6*t^7) )); // G. C. Greubel, Aug 10 2019

(Sage)

def A163878_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^6)/(1-4*t+9*t^6-6*t^7)).list()

A163878_list(30) # G. C. Greubel, Aug 10 2019

(GAP) a:=[5, 20, 80, 320, 1280, 5110];; for n in [7..30] do a[n]:=3*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -6*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 10 2019

CROSSREFS

Sequence in context: A214939 A162925 A163316 * A164354 A164706 A165185

Adjacent sequences:  A163875 A163876 A163877 * A163879 A163880 A163881

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified September 16 18:43 EDT 2019. Contains 327117 sequences. (Running on oeis4.)