A166568 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

1, 14, 182, 2366, 30758, 399854, 5198102, 67575326, 878479238, 11420230094, 148462991222, 1930018885886, 25090245516427, 326173191712368, 4240251492245496, 55123269398992704, 716602502184321480

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 (12,12,12,12,12,12,12,12,12,12,12,-78).

Formula

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

From G. C. Greubel, Dec 03 2024: (Start)

a(n) = 12*Sum_{j=1..11} a(n-j) - 78*a(n-12).

G.f.: (1+x)*(1-x^12)/(1 - 13*x + 90*x^12 - 78*x^13). (End)

Mathematica

coxG[{12, 78, -12}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 03 2015 *)
CoefficientList[Series[(1+t)*(1-t^12)/(1-13*t+90*t^12-78*t^13), {t, 0, 50}], t] (* G. C. Greubel, May 17 2016; Dec 03 2024 *)

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( (1+x)*(1-x^12)/(1-13*x+90*x^12-78*x^13) )); // G. C. Greubel, Dec 03 2024
(SageMath)
def A166568_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^12)/(1-13*x+90*x^12-78*x^13) ).list()
A166568_list(40) # G. C. Greubel, Dec 03 2024

Crossrefs

Cf. A154638, A169452, A170733.

Sequence in context: A165270 A165874 A166379 * A166969 A167115 A167670

Adjacent sequences: A166565 A166566 A166567 * A166569 A166570 A166571

Keyword

nonn

Author

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

Status

approved