A166613 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

1, 26, 650, 16250, 406250, 10156250, 253906250, 6347656250, 158691406250, 3967285156250, 99182128906250, 2479553222656250, 61988830566405925, 1549720764160140000, 38743019104003297200, 968575477600077360000

Offset

0,2

Comments

The initial terms coincide with those of A170745, 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 (24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, -300).

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)/(300*t^12 - 24*t^11 - 24*t^10 - 24*t^9 -24*t^8 -24*t^7 - 24*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 -24*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)/(300*t^12 - 24*t^11 - 24*t^10 - 24*t^9 - 24*t^8 - 24*t^7 - 24*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 19 2016 *)
coxG[{12, 300, -24}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 14 2018 *)

Crossrefs

Sequence in context: A165369 A165973 A166420 * A167079 A167225 A167697

Adjacent sequences: A166610 A166611 A166612 * A166614 A166615 A166616

Keyword

nonn

Author

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

Status

approved