A166165 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 36, 1260, 44100, 1543500, 54022500, 1890787500, 66177562500, 2316214687500, 81067514062500, 2837362992186870, 99307704726518400, 3475769665427372880, 121651938289931061600, 4257817840146642534000, 149023624405099426920000

Offset

0,2

Comments

The initial terms coincide with those of A170755, 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 (34, 34, 34, 34, 34, 34, 34, 34, 34, -595).

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)/(595*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-35*t+629*t^10-595*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-35*t+629*t^10-595*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 06 2016 *)
coxG[{595, 10, -34}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 11 2020 *)

Prog

(Sage)
def A166165_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^10)/(1-35*t+629*t^10-595*t^11) ).list()
A166165_list(30) # G. C. Greubel, Mar 11 2020

Crossrefs

Sequence in context: A164672 A165168 A165651 * A166430 A166688 A167089

Adjacent sequences: A166162 A166163 A166164 * A166166 A166167 A166168

Keyword

nonn

Author

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

Status

approved