A167933 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

1, 21, 420, 8400, 168000, 3360000, 67200000, 1344000000, 26880000000, 537600000000, 10752000000000, 215040000000000, 4300800000000000, 86016000000000000, 1720320000000000000, 34406400000000000000

Offset

0,2

Comments

The initial terms coincide with those of A170740, 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 (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).

Formula

G.f.: (t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*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)/( 190*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).

G.f.: (1+x)*(1-x^16)/(1 -20*x +209*x^16 -190*x^17). - G. C. Greubel, Apr 25 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^16)/(1-20*x+209*x^16-190*x^17), {x, 0, 20}], x] (* G. C. Greubel, Jul 01 2016, modified Apr 25 2019 *)
coxG[{16, 190, -19, 20}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 25 2019 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^16)/(1-20*x+209*x^16-190*x^17)) \\ G. C. Greubel, Apr 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^16)/(1-20*x+209*x^16-190*x^17) )); // G. C. Greubel, Apr 25 2019
(Sage) ((1+x)*(1-x^16)/(1-20*x+209*x^16-190*x^17)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

Crossrefs

Cf. A154638, A170740.

Sequence in context: A167074 A167150 A167681 * A168698 A168746 A168794

Adjacent sequences: A167930 A167931 A167932 * A167934 A167935 A167936

Keyword

nonn

Author

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

Status

approved