A166410 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 16, 240, 3600, 54000, 810000, 12150000, 182250000, 2733750000, 41006250000, 615093750000, 9226406249880, 138396093746400, 2075941406169120, 31139121092133600, 467086816375956000, 7006302245548620000

Offset

0,2

Comments

The initial terms coincide with those of A170735, 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 (14, 14, 14, 14, 14, 14, 14, 14, 14, 14, -105).

Formula

G.f.: (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)/(105*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).

Mathematica

CoefficientList[Series[(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)/(105*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1), {t, 0, 500}], t] (* G. C. Greubel, May 12 2016 *)
coxG[{11, 105, -14}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 24 2021 *)

Crossrefs

Sequence in context: A063814 A165308 A165876 * A166584 A167026 A167117

Adjacent sequences: A166407 A166408 A166409 * A166411 A166412 A166413

Keyword

nonn

Author

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

Status

approved