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A166614
Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.
1
1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332352, 3811511582641152, 99099301148669601, 2576581829865400500, 66991127576500176075, 1741769316988998417900
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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, -325).
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)/(325*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^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^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 19 2016 *)
CROSSREFS
Sequence in context:
A165445
A165979
A166421
*
A167080
A167226
A167698
Adjacent sequences:
A166611
A166612
A166613
*
A166615
A166616
A166617
KEYWORD
nonn
AUTHOR
John Cannon
and
N. J. A. Sloane
, Dec 03 2009
STATUS
approved