A165445 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743201, 146596599314100, 3811511581929675, 99099301124011500, 2576581829064137700, 66991127551503386400, 1741769316230819007600

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..700

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

Formula

G.f.: (t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(325*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).

Maple

seq(coeff(series((x^9+2*x^8+2*x^7+2*x^6+2*x^5+2*x^4+2*x^3+2*x^2+2*x+1 )/(325*x^9-25*x^8-25*x^7-25*x^6-25*x^5-25*x^4-25*x^3-25*x^2 -25*x +1), x, n+1), x, n), n = 0 .. 15); # Muniru A Asiru, Oct 21 2018

Mathematica

coxG[{9, 325, -25}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 21 2017 *)
CoefficientList[Series[(1+t)*(1-t^9)/(1-26*t+350*t^9-325*t^10), {t, 0, 20}], t] (* G. C. Greubel, Oct 20 2018 *)

Prog

(PARI) t='t+O('t^20); Vec((1+t)*(1-t^9)/(1-26*t+350*t^9-325*t^10)) \\ G. C. Greubel, Oct 20 2018
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^9)/(1-26*t+350*t^9-325*t^10) )); // G. C. Greubel, Oct 20 2018
(Sage)
def A165445_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^9)/(1-26*t+350*t^9-325*t^10)).list()
A165445_list(20) # G. C. Greubel, Sep 16 2019
(GAP) a:=[27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743201];; for n in [10..20] do a[n]:=25*Sum([1..8], j-> a[n-j]) -325*a[n-9]; od; Concatenation([1], a); # G. C. Greubel, Sep 16 2019

Crossrefs

Sequence in context: A164017 A164644 A164969 * A165979 A166421 A166614

Adjacent sequences: A165442 A165443 A165444 * A165446 A165447 A165448

Keyword

nonn,easy

Author

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

Status

approved