A166325 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 50, 2450, 120050, 5882450, 288240050, 14123762450, 692064360050, 33911153642450, 1661646528480050, 81420679895521225, 3989613314880480000, 195491052429140580000, 9579061569027744360000, 469374016882352414700000

Offset

0,2

Comments

The initial terms coincide with those of A170769, 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 (48,48,48,48,48,48,48,48,48,-1176).

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)/(1176*t^10 - 48*t^9 - 48*t^8 - 48*t^7 - 48*t^6 - 48*t^5 - 48*t^4 - 48*t^3 - 48*t^2 - 48*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-49*t+1224*t^10-1176*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 12 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-49*t+1224*t^10-1176*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 09 2016 *)
coxG[{10, 1176, -48}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 12 2020 *)

Prog

(Sage)
def A166325_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^10)/(1-49*t+1224*t^10-1176*t^11) ).list()
A166325_list(30) # G. C. Greubel, Aug 10 2019

Crossrefs

Sequence in context: A164695 A165182 A165726 * A166463 A166856 A167103

Adjacent sequences: A166322 A166323 A166324 * A166326 A166327 A166328

Keyword

nonn

Author

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

Status

approved