A162783 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

1, 14, 182, 2275, 28392, 353808, 4408950, 54938520, 684572616, 8530235532, 106292493216, 1324476080928, 16503864518232, 205649272719072, 2562528512535264, 31930831990629936, 397879682765894784

Offset: 0

Author

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

Keywords

• nonn

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..900
• Index entries for linear recurrences with constant coefficients, signature (12, 12, -78).

Programs

GAP

a:=[14, 182, 2275];; for n in [4..20] do a[n]:=12*a[n-1]+12*a[n-2] - 78*a[n-3]; od; Concatenation([1], a); # G. C. Greubel, Apr 26 2019

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^3)/(1-13*x+90*x^3-78*x^4) )); // G. C. Greubel, Apr 26 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^3)/(1-13*x+90*x^3-78*x^4), {x,0,20}],x] (* or *) coxG[{3, 78, -12}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 26 2019 *)

PARI

my(x='x+O('x^20)); Vec((1+x)*(1-x^3)/(1-13*x+90*x^3-78*x^4)) \\ G. C. Greubel, Apr 26 2019

Sage

((1+x)*(1-x^3)/(1-13*x+90*x^3-78*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019

Formula

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(78*t^3 - 12*t^2 - 12*t + 1).

G.f.: (1+x)*(1-x^3)/(1 - 13*x + 90*x^3 - 78*x^4). - G. C. Greubel, Apr 26 2019