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

0,2

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,-210).

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

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 *)

Crossrefs

Sequence in context: A162808 A212335 A342887 * A163514 A163988 A164635

Adjacent sequences: A163146 A163147 A163148 * A163150 A163151 A163152

Keyword

nonn

Author

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

Status

approved