A166615 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698650172, 155653695863554266, 4202649788315954976, 113471544284530509168, 3063731695682316317568

Offset

0,2

Comments

The initial terms coincide with those of A170747, 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 (26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, -351).

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)/(351*t^12 - 26*t^11 - 26*t^10 - 26*t^9 -26*t^8 -26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t +1).

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)/(351*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1), {t, 0, 50}], t](* G. C. Greubel, May 19 2016 *)
coxG[{12, 351, -26}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 22 2020 *)

Crossrefs

Sequence in context: A165456 A165980 A166422 * A167081 A167235 A063817

Adjacent sequences: A166612 A166613 A166614 * A166616 A166617 A166618

Keyword

nonn

Author

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

Status

approved