A166230 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 42, 1722, 70602, 2894682, 118681962, 4865960442, 199504378122, 8179679503002, 335366859623082, 13750041244545501, 563751691026330240, 23113819332078093360, 947666592615142522080, 38854330297218411872400

Offset

0,2

Comments

The initial terms coincide with those of A170761, 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 (40, 40, 40, 40, 40, 40, 40, 40, 40, -820).

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)/(820*t^10 - 40*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-41*t+860*t^10-820*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-41*t+860*t^10-820*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 07 2016 *)
coxG[{10, 820, -40}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 11 2020 *)

Prog

(Sage)
def A166230_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^10)/(1-41*t+860*t^10-820*t^11) ).list()
A166230_list(30) # G. C. Greubel, Mar 11 2020

Crossrefs

Sequence in context: A164686 A165174 A165693 * A166436 A166716 A167095

Adjacent sequences: A166227 A166228 A166229 * A166231 A166232 A166233

Keyword

nonn

Author

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

Status

approved