A165979 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332001, 3811511582622900, 99099301147958475, 2576581829840760300, 66991127575699606500, 1741769316964025575200

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170746, 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 (25, 25, 25, 25, 25, 25, 25, 25, 25, -325).

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11) )); // G. C. Greubel, Apr 26 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11), {x, 0, 20}], x] (* G. C. Greubel, Apr 20 2016, modified Apr 26 2019 *)
coxG[{10, 325, -25}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 26 2019 *)

PARI

my(x='x+O('x^20)); Vec((1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11)) \\ G. C. Greubel, Apr 26 2019

Sage

((1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 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)/(325*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).

G.f.: (1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11). - G. C. Greubel, Apr 26 2019