A165266 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 12, 132, 1452, 15972, 175692, 1932612, 21258732, 233846052, 2572306506, 28295370840, 311249071320, 3423739697400, 37661135713080, 414272482302360, 4556997189369240, 50126967807537720, 551396631852151800

Offset

0,2

Comments

The initial terms coincide with those of A003954, 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..955

Index entries for linear recurrences with constant coefficients, signature (10,10,10,10,10,10,10,10,-55).

Formula

G.f.: (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)/(55*t^9 - 10*t^8 - 10*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^9)/(1-11*t+65*t^9-55*t^10), t, n+1), t, n), n = 0..30); # G. C. Greubel, Sep 25 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^9)/(1-11*t+65*t^9-55*t^10), {t, 0, 30}], t] (* or *) coxG[{9, 55, -10}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 25 2019 *)

Prog

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^9)/(1-11*t+65*t^9-55*t^10)) \\ G. C. Greubel, Sep 25 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^9)/(1-11*t+65*t^9-55*t^10) )); // G. C. Greubel, Sep 25 2019
(Sage)
def A165266_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^9)/(1-11*t+65*t^9-55*t^10)).list()
A165266_list(30) # G. C. Greubel, Sep 25 2019
(GAP) a:=[12, 132, 1452, 15972, 175692, 1932612, 21258732, 233846052, 2572306506];; for n in [10..30] do a[n]:=10*Sum([1..8], j-> a[n-j]) -55*a[n-9]; od; Concatenation([1], a); # G. C. Greubel, Sep 25 2019

Crossrefs

Sequence in context: A063813 A164601 A164781 * A165807 A166372 A166557

Adjacent sequences: A165263 A165264 A165265 * A165267 A165268 A165269

Keyword

nonn

Author

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

Status

approved