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A163995 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I. 1
1, 26, 650, 16250, 406250, 10156250, 253905925, 6347640000, 158690797200, 3967264860000, 99181494750000, 2479534200000000, 61988275781355300, 1549704914070300000, 38742573340231207200, 968563095719204700000, 24214046448355276500000, 605350387594249537500000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170745, 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..710

Index entries for linear recurrences with constant coefficients, signature (24,24,24,24,24,-300).

FORMULA

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(300*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1).

MAPLE

seq(coeff(series((1+t)*(1-t^6)/(1-25*t+324*t^6-300*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^6)/(1-25*t+324*t^6-300*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 24 2017 *)

coxG[{6, 300, -24}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 13 2019 *)

PROG

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-25*t+324*t^6-300*t^7)) \\ G. C. Greubel, Aug 24 2017

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-25*t+324*t^6-300*t^7) )); // G. C. Greubel, Aug 13 2019

(Sage)

def A163995_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^6)/(1-25*t+324*t^6-300*t^7)).list()

A163995_list(30) # G. C. Greubel, Aug 13 2019

(GAP) a:=[26, 650, 16250, 406250, 10156250, 253905925];; for n in [7..30] do a[n]:=24*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -300*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 13 2019

CROSSREFS

Sequence in context: A162812 A163177 A163526 * A164639 A164964 A165369

Adjacent sequences:  A163992 A163993 A163994 * A163996 A163997 A163998

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified September 22 12:52 EDT 2019. Contains 327307 sequences. (Running on oeis4.)