A164630 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 18, 306, 5202, 88434, 1503378, 25557426, 434476089, 7386090912, 125563501440, 2134578775392, 36287826447168, 616892833115424, 10487174482692864, 178281903641223096, 3030791298303722112, 51523433990019421056

Offset

0,2

Comments

The initial terms coincide with those of A170737, 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..16.

Index entries for linear recurrences with constant coefficients, signature (16,16,16,16,16,16,-136).

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(136*t^7 - 16*t^6 -16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).

Mathematica

coxG[{7, 136, -16}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 17 2023 *)

Crossrefs

Sequence in context: A163104 A163452 A163967 * A164892 A165329 A165880

Adjacent sequences: A164627 A164628 A164629 * A164631 A164632 A164633

Keyword

nonn

Author

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

Status

approved