A163149 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 22, 462, 9702, 203511, 4268880, 89544840, 1878307200, 39399681090, 826454197800, 17335839305400, 363639419173800, 7627760320511100, 160001156198268000, 3356210592504924000, 70400425902447564000

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,-210).

Programs

Mathematica

CoefficientList[Series[(t^4 + 2 t^3 + 2 t^2 + 2 t + 1)/(210 t^4 - 20 t^3 - 20 t^2 - 20 t + 1), {t, 0, 16}], t] (* Jinyuan Wang, Mar 23 2020 *)

Formula

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

a(n) = -210*a(n-4) + 20*Sum_{k=1..3} a(n-k). - Wesley Ivan Hurt, May 05 2021