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

Author

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

Keywords

• nonn

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

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

Programs

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 *)

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