A166258 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 45, 1980, 87120, 3833280, 168664320, 7421230080, 326534123520, 14367501434880, 632170063134720, 27815482777926690, 1223881242228730800, 53850774658062239550, 2369434084954654251600, 104255099738001078372000

Offset

0,2

Comments

The initial terms coincide with those of A170764, 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 (43, 43, 43, 43, 43, 43, 43, 43, 43, -946).

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)/(946*t^10 - 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-44*t+989*t^10-946*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-44*t+989*t^10-946*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 08 2016 *)
coxG[{10, 946, -43}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 11 2020 *)

Prog

(SageMath)
def A166258_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^10)/(1-44*t+989*t^10-946*t^11) ).list()
A166258_list(30) # G. C. Greubel, Mar 11 2020
(PARI) Vec((1+x^2+x^4+x^6+x^8)*(1+x)^2/(1-43*x-43*x^2-43*x^3-43*x^4-43*x^5-43*x^6-43*x^7-43*x^8-43*x^9+946*x^10)+O(x^99)) \\ Charles R Greathouse IV, Jun 08 2026

Crossrefs

Cf. A170764, A154638.

Sequence in context: A164690 A165177 A165699 * A166439 A166738 A167098

Adjacent sequences: A166255 A166256 A166257 * A166259 A166260 A166261

Keyword

nonn,easy

Author

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

Status

approved