A165787 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 9, 72, 576, 4608, 36864, 294912, 2359296, 18874368, 150994944, 1207959516, 9663675840, 77309404452, 618475217472, 4947801594624, 39582411595776, 316659283476480, 2533274193494016, 20266192953409536, 162129538870935552

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

G. C. Greubel, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (7,7,7,7,7,7,7,7,7,-28).

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)/(28*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).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-8*t+35*t^10-28*t^11), t, n+1), t, n), n = 0..20); # G. C. Greubel, Aug 10 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-8*t+35*t^10-28*t^11), {t, 0, 20}], t] (* G. C. Greubel, Apr 08 2016 *)
coxG[{10, 28, -7}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 22 2019 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-8*t+35*t^10-28*t^11)) \\ G. C. Greubel, Sep 22 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-8*t+35*t^10-28*t^11) )); // G. C. Greubel, Sep 22 2019
(SageMath)
def A165787_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-8*t+35*t^10-28*t^11)).list()
A165787_list(20) # G. C. Greubel, Sep 22 2019
(GAP) a:=[9, 72, 576, 4608, 36864, 294912, 2359296, 18874368, 150994944, 1207959516];; for n in [11..20] do a[n]:=7*Sum([1..9], j-> a[n-j]) -28*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 22 2019

Crossrefs

Sequence in context: A164375 A164777 A165216 * A166367 A166541 A166924

Adjacent sequences: A165784 A165785 A165786 * A165788 A165789 A165790

Keyword

nonn

Author

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

Status

approved