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A164369
Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
2
1, 7, 42, 252, 1512, 9072, 54432, 326571, 1959300, 11755065, 70525980, 423129420, 2538617760, 15230754000, 91378809060, 548238566925, 3289225689750, 19734119944875, 118397314970550, 710339464409400, 4261770250642800
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003949, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
FORMULA
G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(15*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).
G.f.: (1+x)*(1-x^7)/(1 -6*x +20*x^7 -15*x^8). - G. C. Greubel, Apr 25 2019
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^7)/(1-6*x+20*x^7-15*x^8), {x, 0, 30}], x] (* G. C. Greubel, Sep 17 2017, modified Apr 25 2019 *)
coxG[{7, 15, -5, 30}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 25 2019 *)
PROG
(PARI) my(x='x+O('x^30)); Vec((1+x)*(1-x^7)/(1-6*x+20*x^7-15*x^8)) \\ G. C. Greubel, Sep 17 2017, modified Apr 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^7)/(1-6*x+20*x^7-15*x^8) )); // G. C. Greubel, Apr 25 2019
(Sage) ((1+x)*(1-x^7)/(1-6*x+20*x^7-15*x^8)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019
CROSSREFS
Sequence in context: A094168 A163345 A163923 * A164742 A165214 A165782
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved