A164779 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829645, 430466400, 3874194000, 34867713600, 313809130800, 2824279552800, 25418492355600, 228766218624000, 2058894054430380, 18530029271219040, 166770108473225760

Offset

0,2

Comments

The initial terms coincide with those of A003952, 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..1000

Index entries for linear recurrences with constant coefficients, signature (8, 8, 8, 8, 8, 8, 8, -36).

Formula

G.f.: (t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/( 36*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

G.f.: (1+x)*(1-x^8)/(1 -9*x +44*x^8 -36*x^9). - G. C. Greubel, Apr 26 2019

Mathematica

coxG[{8, 36, -8}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 13 2017 *)
CoefficientList[Series[(1+x)*(1-x^8)/(1-9*x+44*x^8-36*x^9), {x, 0, 20}], x] (* G. C. Greubel, Apr 26 2019 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^8)/(1-9*x+44*x^8-36*x^9)) \\ G. C. Greubel, Apr 26 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^8)/(1-9*x+44*x^8-36*x^9) )); // G. C. Greubel, Apr 26 2019
(Sage) ((1+x)*(1-x^8)/(1-9*x+44*x^8-36*x^9)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019

Crossrefs

Sequence in context: A163397 A163954 A164548 * A165219 A165788 A166368

Adjacent sequences: A164776 A164777 A164778 * A164780 A164781 A164782

Keyword

nonn

Author

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

Status

approved