A166303 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 46, 2070, 93150, 4191750, 188628750, 8488293750, 381973218750, 17188794843750, 773495767968750, 34807309558592715, 1566328930136625600, 70484801856146057160, 3171816083526478304400, 142731723758687281647000

Offset

0,2

Comments

The initial terms coincide with those of A170765, 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 (44, 44, 44, 44, 44, 44, 44, 44, 44, -990).

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)/(990*t^10 - 44*t^9 - 44*t^8 - 44*t^7 - 44*t^6 - 44*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-45*t+1034*t^10-990*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-45*t+1034*t^10-990*t^11), {t, 0, 30}], t] (* G. C. Greubel, May 09 2016 *)
coxG[{10, 990, -44}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 11 2020 *)

Prog

(SageMath)
def A166303_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-45*t+1034*t^10-990*t^11)).list()
A166303_list(30) # G. C. Greubel, Mar 11 2020
(PARI) Vec((1+x^2+x^4+x^6+x^8)*(1+x)^2/(1-44*x-44*x^2-44*x^3-44*x^4-44*x^5-44*x^6-44*x^7-44*x^8-44*x^9+990*x^10)+O(x^99)) \\ Charles R Greathouse IV, Jun 08 2026

Crossrefs

Cf. A170765, A154638.

Sequence in context: A164691 A165178 A165702 * A166440 A166739 A167099

Adjacent sequences: A166300 A166301 A166302 * A166304 A166305 A166306

Keyword

nonn,easy

Author

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

Status

approved