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

0,2

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.

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).

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

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 *)

Prog

(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
(Magma) R<x>:=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
(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

Crossrefs

Sequence in context: A164835 A165270 A165874 * A166568 A166969 A167115

Adjacent sequences: A166376 A166377 A166378 * A166380 A166381 A166382

Keyword

nonn,easy

Author

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

Status

approved