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.

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.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5, 5, 5, 5, 5, 5, -15).

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

Adjacent sequences: A164366 A164367 A164368 * A164370 A164371 A164372

Keyword

nonn

Author

John Cannon and N. J. A. Sloane, Dec 03 2009

Status

approved