A166723 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

1, 44, 1892, 81356, 3498308, 150427244, 6468371492, 278139974156, 11960018888708, 514280812214444, 22114074925221092, 950905221784506956, 40888924536733798162, 1758223755079553280288, 75603621468420789304176

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170763, 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 (42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, -903).

Programs

Mathematica

CoefficientList[Series[(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)/(903*t^12 - 42*t^11 - 42*t^10 - 42*t^9 - 42*t^8 - 42*t^7 - 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 24 2016 *)
coxG[{12,903,-42}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 03 2023 *)

Formula

G.f.: (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)/(903*t^12 - 42*t^11 - 42*t^10 - 42*t^9 -42*t^8 -42*t^7 -42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1).