A166172 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 40, 1560, 60840, 2372760, 92537640, 3608967960, 140749750440, 5489240267160, 214080370419240, 8349134446349580, 325616243407603200, 12699033492895339200, 495262306222871990400, 19315229942690204328000

Offset

0,2

Comments

The initial terms coincide with those of A170759, 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..500

Index entries for linear recurrences with constant coefficients, signature (38, 38, 38, 38, 38, 38, 38, 38, 38, -741).

Formula

G.f.: (t^10 + 2*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)/(741*t^10 - 38*t^9 - 38*t^8 - 38*t^7 - 38*t^6 - 38*t^5 - 38*t^4 - 38*t^3 - 38*t^2 - 38*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-39*t+779*t^10-741*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-39*t+779*t^10-741*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 06 2016 *)
coxG[{10, 741, -38}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 31 2017 *)

Prog

(Sage)
def A163878_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^10)/(1-39*t+779*t^10-741*t^11) ).list()
A163878_list(30) # G. C. Greubel, Aug 10 2019

Crossrefs

Sequence in context: A164684 A165172 A165690 * A166434 A166693 A167093

Adjacent sequences: A166169 A166170 A166171 * A166173 A166174 A166175

Keyword

nonn

Author

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

Status

approved