A166610 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

1, 23, 506, 11132, 244904, 5387888, 118533536, 2607737792, 57370231424, 1262145091328, 27767192009216, 610878224202752, 13439320932460291, 295665060514120836, 6504631331310536193, 143101889288829107868

Offset

0,2

Comments

The initial terms coincide with those of A170742, 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 (21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -231).

Formula

G.f.: (t^12 + 2*t^11 + 2*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)/(231*t^12 - 21*t^11 - 21*t^10 - 21*t^9 -21*t^8 -21*t^7 - 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 -21*t + 1).

G.f.: (1+x)*(1-x^12)/(1 -22*x + 252*x^12 - 231*x^13). - G. C. Greubel, Apr 25 2019

Mathematica

coxG[{12, 231, -21}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 03 2015 *)
CoefficientList[Series[(1+x)*(1-x^12)/(1-22*x+252*x^12-231*x^13), {x, 0, 20}], x] (* G. C. Greubel, May 18 2016, modified Apr 25 2019 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^12)/(1-22*x+252*x^12-231*x^13)) \\ G. C. Greubel, Apr 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^12)/(1-22*x+252*x^12-231*x^13) )); // G. C. Greubel, Apr 25 2019
(Sage) ((1+x)*(1-x^12)/(1-22*x+252*x^12-231*x^13)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

Crossrefs

Sequence in context: A165365 A165939 A166417 * A167076 A167174 A167694

Adjacent sequences: A166607 A166608 A166609 * A166611 A166612 A166613

Keyword

nonn

Author

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

Status

approved