A165180 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402335792, 24317909781096, 1142941759658496, 53718262701458688, 2524758346851499008, 118663642296518664960, 5577191187677793197568, 262127985808702829674752

Offset

0,2

Comments

The initial terms coincide with those of A170767, 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..14.

Index entries for linear recurrences with constant coefficients, signature (46, 46, 46, 46, 46, 46, 46, -1081).

Formula

G.f.: (t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1081*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).

a(n) = -1081*a(n-8) + 46*Sum_{k=1..7} a(n-k). - Wesley Ivan Hurt, Sep 04 2022

Mathematica

With[{num=Total[2t^Range[7]]+t^8+1, den=Total[-46 t^Range[7]]+1081t^8+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Jul 27 2011 *)

Crossrefs

Sequence in context: A163829 A164348 A164693 * A165708 A166313 A166442

Adjacent sequences: A165177 A165178 A165179 * A165181 A165182 A165183

Keyword

nonn

Author

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

Status

approved