login
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.
2
1, 14, 182, 2275, 28392, 353808, 4408950, 54938520, 684572616, 8530235532, 106292493216, 1324476080928, 16503864518232, 205649272719072, 2562528512535264, 31930831990629936, 397879682765894784
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.
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
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 *)
PROG
(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
(Magma) R<x>:=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
(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
(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
CROSSREFS
Sequence in context: A230055 A133286 A163416 * A199942 A097828 A030008
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved