A166910 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

1, 8, 56, 392, 2744, 19208, 134456, 941192, 6588344, 46118408, 322828856, 2259801992, 15818613944, 110730297580, 775112082864, 5425784578704, 37980492041520, 265863444224784, 1861044109112496, 13027308760560528

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A003950, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -21).

Programs

Mathematica

CoefficientList[Series[(t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(21*t^13 - 6*t^12 - 6*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 28 2016 *)
coxG[{13,21,-6}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 05 2021 *)

Formula

G.f.: (t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(21*t^13 - 6*t^12 - 6*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).