A165939 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 23, 506, 11132, 244904, 5387888, 118533536, 2607737792, 57370231424, 1262145091328, 27767192008963, 610878224191620, 13439320932093441, 295665060503367324, 6504631331014936812, 143101889281027434912

Offset

0,2

Comments

The initial terms coincide with those of A170742, 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 (21,21,21,21,21,21,21,21,21,-231).

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)/(231*t^10 - 21*t^9 - 21*t^8 - 21*t^7 - 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-22*t+252*t^10-231*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Sep 25 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-22*t+252*t^10-231*t^11), {t, 0, 25}], t] (* G. C. Greubel, Apr 18 2016 *)
coxG[{10, 231, -21}] (* 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^10)/(1-22*t+252*t^10-231*t^11)) \\ G. C. Greubel, Sep 25 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-22*t+252*t^10-231*t^11) )); // G. C. Greubel, Sep 25 2019
(Sage)
def A165939_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-22*t+252*t^10-231*t^11)).list()
A165939_list(30) # G. C. Greubel, Sep 25 2019
(GAP) a:=[23, 506, 11132, 244904, 5387888, 118533536, 2607737792, 57370231424, 1262145091328, 27767192008963];; for n in [11..30] do a[n]:=21*Sum([1..9], j-> a[n-j]) -231*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 25 2019

Crossrefs

Sequence in context: A164636 A164957 A165365 * A166417 A166610 A167076

Adjacent sequences: A165936 A165937 A165938 * A165940 A165941 A165942

Keyword

nonn

Author

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

Status

approved