A165172 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 40, 1560, 60840, 2372760, 92537640, 3608967960, 140749750440, 5489240266380, 214080370358400, 8349134442792000, 325616243222649600, 12699033483880036800, 495262305800992828800, 19315229923495904673600

Offset

0,2

Comments

The initial terms coincide with those of A170759, 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 (38, 38, 38, 38, 38, 38, 38, -741).

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)/(741*t^8 - 38*t^7 - 38*t^6 - 38*t^5 - 38*t^4 - 38*t^3 - 38*t^2 - 38*t + 1).

a(n) = -741*a(n-8) + 38*Sum_{k=1..7} a(n-k). - Wesley Ivan Hurt, Apr 25 2023

Crossrefs

Sequence in context: A163669 A164085 A164684 * A165690 A166172 A166434

Adjacent sequences: A165169 A165170 A165171 * A165173 A165174 A165175

Keyword

nonn

Author

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

Status

approved