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A167093
Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.
1
1, 40, 1560, 60840, 2372760, 92537640, 3608967960, 140749750440, 5489240267160, 214080370419240, 8349134446350360, 325616243407664040, 12699033492898897560, 495262306223057004060, 19315229942699223127920
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170759, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, -741).
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)/(741*t^13 - 38*t^12 - 38*t^11 - 38*t^10 - 38*t^9 - 38*t^8 - 38*t^7 - 38*t^6 - 38*t^5 - 38*t^4 - 38*t^3 - 38*t^2 - 38*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)/(741*t^13 - 38*t^12 - 38*t^11 - 38*t^10 - 38*t^9 - 38*t^8 - 38*t^7 - 38*t^6 - 38*t^5 - 38*t^4 - 38*t^3 - 38*t^2 - 38*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Jun 02 2016 *)
CROSSREFS
Sequence in context: A166172 A166434 A166693 * A167538 A167829 A167956
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved