A169018 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.

1, 5, 20, 80, 320, 1280, 5120, 20480, 81920, 327680, 1310720, 5242880, 20971520, 83886080, 335544320, 1342177280, 5368709120, 21474836480, 85899345920, 343597383680, 1374389534720, 5497558138880, 21990232555520, 87960930222080

Offset

0,2

Comments

The initial terms coincide with those of A003947, although the two sequences are eventually different.

First disagreement at index 24: a(24) = 351843720888310, A003947(24) = 351843720888320. - Klaus Brockhaus, Apr 20 2011

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

Links

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -6).

Formula

G.f.: (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)/(6*t^24 - 3*t^23 - 3*t^22 - 3*t^21 - 3*t^20 - 3*t^19 - 3*t^18 - 3*t^17 - 3*t^16 - 3*t^15 - 3*t^14 - 3*t^13 - 3*t^12 - 3*t^11 - 3*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1).

Mathematica

coxG[{24, 6, -3, 30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 25 2015 *)

Crossrefs

Cf. A003947 (G.f.: (1+x)/(1-4*x)).

Sequence in context: A168874 A168922 A168970 * A169066 A169114 A169162

Adjacent sequences: A169015 A169016 A169017 * A169019 A169020 A169021

Keyword

nonn

Author

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

Status

approved