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A163954 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I. 1
1, 10, 90, 810, 7290, 65610, 590445, 5313600, 47818800, 430336800, 3872739600, 34852032000, 313644670380, 2822589491040, 25401392681760, 228595320793440, 2057202978723360, 18513432737727840, 166608348947205840 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A003952, 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 (8,8,8,8,8,-36).

FORMULA

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

MAPLE

seq(coeff(series((1+t)*(1-t^6)/(1-9*t+44*t^6-36*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 10 2019

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^6)/(1-9*t+44*t^6-36*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 13 2017 *)

coxG[{6, 36, -8}] (* 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)/(1-9*t+44*t^6-36*t^7)) \\ G. C. Greubel, Aug 13 2017

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-9*t+44*t^6-36*t^7) )); // G. C. Greubel, Aug 10 2019

(Sage)

def A163954_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^6)/(1-9*t+44*t^6-36*t^7)).list()

A163954_list(30) # G. C. Greubel, Aug 10 2019

(GAP) a:=[10, 90, 810, 7290, 65610, 590445];; for n in [7..30] do a[n]:=8*(a[n-1]+a[n-2]+a[n-3]+a[n-4]+a[n-5]) -36*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 10 2019

CROSSREFS

Sequence in context: A010576 A162983 A163397 * A164548 A164779 A165219

Adjacent sequences:  A163951 A163952 A163953 * A163955 A163956 A163957

KEYWORD

nonn,changed

AUTHOR

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

STATUS

approved

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Last modified August 24 16:21 EDT 2019. Contains 326295 sequences. (Running on oeis4.)