A165687 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 38, 1406, 52022, 1924814, 71218118, 2635070366, 97497603542, 3607411331054, 133474219248295, 4938546112160904, 182726206148991744, 6760869627477111480, 250152176215336551984, 9255630519918739230696

Offset

0,2

Comments

The initial terms coincide with those of A170757, 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 (36, 36, 36, 36, 36, 36, 36, 36, -666).

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)/(666*t^9 - 36*t^8 - 36*t^7 - 36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 -

36*t^2 - 36*t + 1)

Mathematica

coxG[{9, 666, -36}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 09 2018 *)

Crossrefs

Sequence in context: A164071 A164674 A165170 * A166170 A166432 A166690

Adjacent sequences: A165684 A165685 A165686 * A165688 A165689 A165690

Keyword

nonn

Author

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

Status

approved