A164684 - OEIS

A164684

Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 40, 1560, 60840, 2372760, 92537640, 3608967960, 140749749660, 5489240206320, 214080366860880, 8349134261335920, 325616234388803280, 12699033070834721520, 495262287019738489680, 19315229086799991370740

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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,-741).

FORMULA

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

MATHEMATICA

coxG[{7, 741, -38}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 29 2021 *)

CROSSREFS

Sequence in context: A163223 A163669 A164085 * A165172 A165690 A166172

Adjacent sequences: A164681 A164682 A164683 * A164685 A164686 A164687

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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