A169369 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

1, 20, 380, 7220, 137180, 2606420, 49521980, 940917620, 17877434780, 339671260820, 6453753955580, 122621325156020, 2329805177964380, 44266298381323220, 841059669245141180, 15980133715657682420, 303622540597495965980, 5768828271352423353620, 109607737155696043718780

Offset

0,2

Comments

The initial terms coincide with those of A170739, although the two sequences are eventually different.

First disagreement at index 31: a(31) = 4609332357943904300910190388118665867830, A170739(31) = 4609332357943904300910190388118665868020. - Klaus Brockhaus, Jun 17 2011

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

Links

Table of n, a(n) for n=0..18.

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

Formula

G.f.: (t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*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^31 - 18*t^30 - 18*t^29 - 18*t^28 - 18*t^27 - 18*t^26 - 18*t^25 - 18*t^24 - 18*t^23 - 18*t^22 - 18*t^21 - 18*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[{31, 171, -18}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 03 2015 *)

Crossrefs

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

Sequence in context: A170605 A170653 A170701 * A169417 A170739 A218722

Adjacent sequences: A169366 A169367 A169368 * A169370 A169371 A169372

Keyword

nonn,easy

Author

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

Extensions

a(16)-a(18) from Stefano Spezia, Dec 09 2025

Status

approved