A166379 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 14, 182, 2366, 30758, 399854, 5198102, 67575326, 878479238, 11420230094, 148462991222, 1930018885795, 25090245514152, 326173191668688, 4240251491494200, 55123269386840928, 716602501995344328

Offset: 0

Author

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

Keywords

• nonn
• easy

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, 12, -78).

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^11)/(1-13*x+90*x^11-78*x^12) )); // G. C. Greubel, Apr 26 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^11)/(1 -13*x +90*x^11 -78*x^12), {x, 0, 20}], x] (* G. C. Greubel, May 10 2016, modified Apr 26 2019 *)
coxG[{11,78,-12}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 30 2016 *)

PARI

my(x='x+O('x^20)); Vec((1+x)*(1-x^11)/(1-13*x+90*x^11-78*x^12)) \\ G. C. Greubel, Apr 26 2019

Sage

((1+x)*(1-x^11)/(1-13*x+90*x^11-78*x^12)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019

Formula

G.f.: (t^11 + 2*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^11 - 12*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).

G.f.: (1+x)*(1-x^11)/(1 -13*x +90*x^11 -78*x^12). - G. C. Greubel, Apr 26 2019

a(n) = -78*a(n-11) + 12*Sum_{k=1..10} a(n-k). - Wesley Ivan Hurt, May 06 2021