A168841 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = 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.

First disagreement at index 20: a(20) = 39568393113206271782479390, A170739(20) = 39568393113206271782479580. - Klaus Brockhaus, Apr 02 2011

Computed with MAGMA using commands similar to those used to compute A154638.

Links

Table of n, a(n) for n=0..15.

Index entries for linear recurrences with constant coefficients, signature (18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, -171).

Formula

G.f.: (t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*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^20 - 18*t^19 - 18*t^18 - 18*t^17 - 18*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).

Mathematica

coxG[{20, 171, -18}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 06 2023 *)

Crossrefs

Cf. A170739 (G.f.: (1+x)/(1-19*x)).

Sequence in context: A168697 A168745 A168793 * A168889 A168937 A168985

Adjacent sequences: A168838 A168839 A168840 * A168842 A168843 A168844

Keyword

nonn

Author

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

Status

approved