A164635 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854431, 39623938200, 832102600560, 17474152477320, 366957157200480, 7706099359922040, 161828066791314000, 3398388987509621490, 71366160020435695800

Offset

0,2

Comments

The initial terms coincide with those of A170741, although the two sequences are eventually different.

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 (20, 20, 20, 20, 20, 20, -210).

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(210*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).

a(n) = -210*a(n-7) + 20*Sum_{k=1..6} a(n-k). - Wesley Ivan Hurt, May 05 2021

Mathematica

coxG[{7, 210, -20}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 11 2015 *)

Crossrefs

Sequence in context: A163149 A163514 A163988 * A164956 A165364 A165895

Adjacent sequences: A164632 A164633 A164634 * A164636 A164637 A164638

Keyword

nonn

Author

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

Status

approved