A165881 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 19, 342, 6156, 110808, 1994544, 35901792, 646232256, 11632180608, 209379250944, 3768826516821, 67838877299700, 1221099791339367, 21979796243114412, 395636332358163924, 7121453982124831776

Offset

0,2

Comments

The initial terms coincide with those of A170738, 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 (17,17,17,17,17,17,17,17,17,-153).

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)/(153*t^10 - 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-18*t+170*t^10-153*t^11), t, n+1), t, n), n = 0..20); # G. C. Greubel, Sep 24 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-18*t+170*t^10-153*t^11), {t, 0, 20}], t] (* G. C. Greubel, Apr 17 2016 *)
coxG[{10, 153, -17}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 23 2017 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-18*t+170*t^10-153*t^11)) \\ G. C. Greubel, Sep 24 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-18*t+170*t^10-153*t^11) )); // G. C. Greubel, Sep 24 2019
(SageMath)
def A163878_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-18*t+170*t^10-153*t^11)).list()
A163878_list(20) # G. C. Greubel, Sep 24 2019
(GAP) a:=[19, 342, 6156, 110808, 1994544, 35901792, 646232256, 11632180608, 209379250944, 3768826516821];; for n in [11..20] do a[n]:=17*Sum([1..9], j-> a[n-j]) -153*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 24 2019

Crossrefs

Cf. A154638, A170738.

Sequence in context: A164631 A164909 A165341 * A166413 A166600 A167049

Adjacent sequences: A165878 A165879 A165880 * A165882 A165883 A165884

Keyword

nonn

Author

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

Status

approved