A165782 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 7, 42, 252, 1512, 9072, 54432, 326592, 1959552, 11757312, 70543851, 423262980, 2539577145, 15237458460, 91424724300, 548548187040, 3291288169680, 19747723302720, 118486305524160, 710917627392000, 4265504529834660

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..500

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

Formula

G.f.: (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)/(15*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-6*t+15*t^10-6*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Sep 22 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-6*t+15*t^10-6*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 08 2016 *)
coxG[{10, 15, -5}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 22 2019 *)

Prog

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-6*t+15*t^10-6*t^11)) \\ G. C. Greubel, Aug 07 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-6*t+15*t^10-6*t^11) )); // G. C. Greubel, Sep 22 2019
(Sage)
def A165782_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^10)/(1-6*t+15*t^10-6*t^11) ).list()
A165782_list(30) # G. C. Greubel, Sep 22 2019
(GAP) a:=[7, 42, 252, 1512, 9072, 54432, 326592, 1959552, 11757312, 70543851];; for n in [11..30] do a[n]:=5*Sum([1..9], j-> a[n-j]) -15*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 22 2019

Crossrefs

Sequence in context: A164369 A164742 A165214 * A166365 A166518 A166878

Adjacent sequences: A165779 A165780 A165781 * A165783 A165784 A165785

Keyword

nonn

Author

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

Status

approved