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A164017 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I. 1
1, 27, 702, 18252, 474552, 12338352, 320796801, 8340707700, 216858163275, 5638306085100, 146595798051300, 3811486585140000, 99098542944724050, 2576559301574090625, 66990468651299212500, 1741750282005552804375 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170746, 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..705

Index entries for linear recurrences with constant coefficients, signature (25,25,25,25,25,-325).

FORMULA

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(325*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).

MAPLE

seq(coeff(series((1+t)*(1-t^6)/(1-26*t+350*t^6-325*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019

MATHEMATICA

coxG[{6, 325, -25}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 26 2017 *)

CoefficientList[Series[(1+t)*(1-t^6)/(1-26*t+350*t^6-325*t^7), {t, 0, 30}], t] (* G. C. Greubel, Sep 07 2017 *)

PROG

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-26*t+350*t^6-325*t^7)) \\ G. C. Greubel, Sep 07 2017

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-26*t+350*t^6-325*t^7) )); // G. C. Greubel, Aug 13 2019

(Sage)

def A164017_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^6)/(1-26*t+350*t^6-325*t^7)).list()

A164017_list(30) # G. C. Greubel, Aug 13 2019

(GAP) a:=[27, 702, 18252, 474552, 12338352, 320796801];; for n in [7..30] do a[n]:=25*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -325*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 13 2019

CROSSREFS

Sequence in context: A162827 A163179 A163527 * A164644 A164969 A165445

Adjacent sequences:  A164014 A164015 A164016 * A164018 A164019 A164020

KEYWORD

nonn,changed

AUTHOR

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

STATUS

approved

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Last modified August 18 15:00 EDT 2019. Contains 326106 sequences. (Running on oeis4.)