A165874 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 14, 182, 2366, 30758, 399854, 5198102, 67575326, 878479238, 11420230094, 148462991131, 1930018883520, 25090245470472, 326173190917392, 4240251479342424, 55123269197863776, 716602499135588520

Offset

0,2

Comments

The initial terms coincide with those of A170733, 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 (12,12,12,12,12,12,12,12,12,-78).

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)/(78*t^10 - 12*t^9 - 12*t^8 - 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-13*t+90*t^10-78*t^11), t, n+1), t, n), n = 0..20); # G. C. Greubel, Sep 23 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-13*t+90*t^10-78*t^11), {t, 0, 25}], t] (* G. C. Greubel, Apr 17 2016 *)
coxG[{10, 78, -12}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 23 2019 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-13*t+90*t^10-78*t^11)) \\ G. C. Greubel, Sep 23 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-13*t+90*t^10-78*t^11) )); // G. C. Greubel, Sep 23 2019
(Sage)
def A165874_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-13*t+90*t^10-78*t^11)).list()
A165874_list(20) # G. C. Greubel, Sep 23 2019
(GAP) a:=[14, 182, 2366, 30758, 399854, 5198102, 67575326, 878479238, 11420230094, 148462991131];; for n in [11..20] do a[n]:=12*Sum([1..9], j-> a[n-j]) -78*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 23 2019

Crossrefs

Sequence in context: A164618 A164835 A165270 * A166379 A166568 A166969

Adjacent sequences: A165871 A165872 A165873 * A165875 A165876 A165877

Keyword

nonn

Author

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

Status

approved