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A166924
Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.
1
1, 9, 72, 576, 4608, 36864, 294912, 2359296, 18874368, 150994944, 1207959552, 9663676416, 77309411328, 618475290588, 4947802324416, 39582418593060, 316659348726336, 2533274789665536, 20266198316163072, 162129586520014848
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003951, 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 (7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, -28).
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)/(28*t^13 - 7*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*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)/(28*t^13 - 7*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 28 2016 *)
coxG[{13, 28, -7}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 12 2023 *)
CROSSREFS
Sequence in context: A165787 A166367 A166541 * A167110 A167658 A167900
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved