A165695 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 44, 1892, 81356, 3498308, 150427244, 6468371492, 278139974156, 11960018888708, 514280812213498, 22114074925139736, 950905221779260440, 40888924536433025976, 1758223755063387680376, 75603621467586675482712

Offset

0,2

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

Table of n, a(n) for n=0..14.

Index entries for linear recurrences with constant coefficients, signature (42, 42, 42, 42, 42, 42, 42, 42, -903).

Formula

G.f. (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^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)

Mathematica

coxG[{9, 903, -42}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 08 2020 *)

Crossrefs

Sequence in context: A164277 A164688 A165176 * A166254 A166438 A166723

Adjacent sequences: A165692 A165693 A165694 * A165696 A165697 A165698

Keyword

nonn

Author

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

Status

approved