A166233 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 43, 1806, 75852, 3185784, 133802928, 5619722976, 236028364992, 9913191329664, 416354035845888, 17486869505526393, 734448519232070580, 30846837807745372371, 1295567187925238776044, 54413821892857220325252

Offset

0,2

Comments

The initial terms coincide with those of A170762, 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 (41, 41, 41, 41, 41, 41, 41, 41, 41, -861).

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)/(861*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-42*t+902*t^10-861*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-42*t+902*t^10-861*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 07 2016 *)
coxG[{10, 861, -41}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 10 2018 *)

Prog

(Sage)
def A166233_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^10)/(1-42*t+902*t^10-861*t^11) ).list()
A166233_list(30) # G. C. Greubel, Aug 10 2019

Crossrefs

Sequence in context: A164687 A165175 A165694 * A166437 A166717 A167096

Adjacent sequences: A166230 A166231 A166232 * A166234 A166235 A166236

Keyword

nonn

Author

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

Status

approved