A167080 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332352, 3811511582641152, 99099301148669952, 2576581829865418401, 66991127576500869300, 1741769316989022364875

Offset

0,2

Comments

The initial terms coincide with those of A170746, 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 (25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, -325).

Formula

G.f.: (t^13 + 2*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)/(325*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).

Mathematica

CoefficientList[Series[(t^13 + 2*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)/(325*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 31 2016 *)

Crossrefs

Sequence in context: A165979 A166421 A166614 * A167226 A167698 A167942

Adjacent sequences: A167077 A167078 A167079 * A167081 A167082 A167083

Keyword

nonn

Author

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

Status

approved