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

Author

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

Keywords

• nonn

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

• Index entries for linear recurrences with constant coefficients, signature (20, 20, 20, 20, 20, 20, -210).

Programs

Mathematica

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

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