A166308 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 47, 2162, 99452, 4574792, 210440432, 9680259872, 445291954112, 20483429889152, 942237774900992, 43342937645444551, 1993775131690399620, 91713656057756096205, 4218828178656675254940, 194066096218202223884700

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170766, 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 (45, 45, 45, 45, 45, 45, 45, 45, 45, -1035).

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^10)/(1-46*x+1080*x^10-1035*x^11) )); // G. C. Greubel, Apr 25 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^10)/(1-46*x+1080*x^10-1035*x^11), {x, 0, 20}], x] (* G. C. Greubel, May 09 2016, modified Apr 25 2019 *)
coxG[{10,1035,-45}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 07 2017 *)

PARI

my(x='x+O('x^20)); Vec((1+x)*(1-x^10)/(1-46*x+1080*x^10 -1035*x^11)) \\ G. C. Greubel, Apr 25 2019

Sage

((1+x)*(1-x^10)/(1-46*x+1080*x^10-1035*x^11)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

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)/(1035*t^10 - 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).

G.f.: (1+x)*(1-x^10)/(1 -46*x +1080*x^10 -1035*x^11). - G. C. Greubel, Apr 25 2019