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A166969 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I. 1
1, 14, 182, 2366, 30758, 399854, 5198102, 67575326, 878479238, 11420230094, 148462991222, 1930018885886, 25090245516518, 326173191714643, 4240251492289176, 55123269399744000, 716602502196473256 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170733, 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 (12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, -78).
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)/(78*t^13 - 12*t^12 - 12*t^11 - 12*t^10 - 12*t^9 - 12*t^8 - 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*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)/(78*t^13 - 12*t^12 - 12*t^11 - 12*t^10 - 12*t^9 - 12*t^8 - 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 29 2016 *)
coxG[{13, 78, -12}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 11 2020 *)
CROSSREFS
Sequence in context: A165874 A166379 A166568 * A167115 A167670 A167922
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved

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Last modified May 21 19:35 EDT 2024. Contains 372738 sequences. (Running on oeis4.)