A168860 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

1, 39, 1482, 56316, 2140008, 81320304, 3090171552, 117426518976, 4462207721088, 169563893401344, 6443427949251072, 244850262071540736, 9304309958718547968, 353563778431304822784, 13435423580389583265792

Offset

0,2

Comments

The initial terms coincide with those of A170758, although the two sequences are eventually different.

First disagreement at index 20: a(20) = 40453205692646545149570675375387, A170758(20) = 40453205692646545149570675376128 . - Klaus Brockhaus, Apr 04 2011

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

Links

Table of n, a(n) for n=0..14.

Index entries for linear recurrences with constant coefficients, signature (37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, -703).

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)/(703*t^20 - 37*t^19 - 37*t^18 - 37*t^17 - 37*t^16 - 37*t^15 - 37*t^14 - 37*t^13 - 37*t^12 - 37*t^11 - 37*t^10 - 37*t^9 - 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1).

Mathematica

coxG[{20, 703, -37}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 21 2015 *)

Crossrefs

Cf. A170758 (G.f.: (1+x)/(1-38*x)).

Sequence in context: A168716 A168764 A168812 * A168908 A168956 A169004

Adjacent sequences: A168857 A168858 A168859 * A168861 A168862 A168863

Keyword

nonn

Author

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

Status

approved