A167931 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

1, 20, 380, 7220, 137180, 2606420, 49521980, 940917620, 17877434780, 339671260820, 6453753955580, 122621325156020, 2329805177964380, 44266298381323220, 841059669245141180, 15980133715657682420

Offset

0,2

Comments

The initial terms coincide with those of A170739, 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 (18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, -171).

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)/( 171*t^16 - 18*t^15 - 18*t^14 - 18*t^13 - 18*t^12 - 18*t^11 - 18*t^10 - 18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1).

G.f.: (1+x)*(1-x^16)/(1 -19*x +189*x^16 -171*x^17). - G. C. Greubel, Apr 25 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^16)/(1-19*x+189*x^16-171*x^17), {x, 0, 20}], x] (* G. C. Greubel, Jul 01 2016, modified Apr 25 2019 *)
coxG[{16, 171, -18, 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)/(1-19*x+189*x^16-171*x^17)) \\ G. C. Greubel, Apr 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^16)/(1-19*x+189*x^16-171*x^17) ));  // G. C. Greubel, Apr 25 2019
(Sage) ((1+x)*(1-x^16)/(1-19*x+189*x^16-171*x^17)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

Crossrefs

Cf. A154638, A170739.

Sequence in context: A167073 A167148 A167680 * A168697 A168745 A168793

Adjacent sequences: A167928 A167929 A167930 * A167932 A167933 A167934

Keyword

nonn

Author

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

Status

approved