A165788 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204845, 34867843200, 313810585200, 2824295234400, 25418656818000, 228767908737600, 2058911155018800, 18530200182592800, 166771799730147600

Offset

0,2

Comments

The initial terms coincide with those of A003952, 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 (8,8,8,8,8,8,8,8,8,-36).

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)/(36*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-9*t+44*t^10-36*t^11), t, n+1), t, n), n = 0..20); # G. C. Greubel, Aug 10 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-9*t+44*t^10-36*t^11), {t, 0, 25}], t] (* G. C. Greubel, Apr 08 2016 *)
coxG[{10, 36, -8}] (* 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)/(1-9*t+44*t^10-36*t^11)) \\ G. C. Greubel, Sep 22 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-9*t+44*t^10-36*t^11) )); // G. C. Greubel, Sep 22 2019
(Sage)
def A165788_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-9*t+44*t^10-36*t^11)).list()
A165788_list(20) # G. C. Greubel, Sep 22 2019
(GAP) a:=[10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204845];; for n in [11..20] do a[n]:=8*Sum([1..9], j-> a[n-j]) -36*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 22 2019

Crossrefs

Sequence in context: A164548 A164779 A165219 * A166368 A166543 A166933

Adjacent sequences: A165785 A165786 A165787 * A165789 A165790 A165791

Keyword

nonn

Author

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

Status

approved