A166583 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

1, 15, 210, 2940, 41160, 576240, 8067360, 112943040, 1581202560, 22136835840, 309915701760, 4338819824640, 60743477544855, 850408685626500, 11905721598750525, 166680102382220700, 2333521433347076700

Offset

0,2

Comments

The initial terms coincide with those of A170734, 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 (13,13,13,13,13,13,13,13,13,13,13,-91).

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)/(91*t^12 - 13*t^11 - 13*t^10 - 13*t^9 - 13*t^8 - 13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t +1).

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

a(n) = 13*Sum_{j=1..11} a(n-j) - 91*a(n-12).

G.f.: (1+x)*(1-x^12)/(1 - 14*x + 104*x^12 - 91*x^13). (End)

Mathematica

CoefficientList[Series[(1+x)*(1-x^12)/(1 - 14*x + 104*x^12 - 91*x^13), {t, 0, 50}], t] (* G. C. Greubel, May 17 2016; Dec 03 2024 *)
coxG[{12, 91, -13}] (* The coxG program is at A169452 *) (* G. C. Greubel, Dec 03 2024 *)

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( (1+x)*(1-x^12)/(1-14*x+104*x^12-91*x^13) )); // G. C. Greubel, Dec 03 2024
(SageMath)
def A166583_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^12)/(1-14*x+104*x^12-91*x^13) ).list()
A166583_list(40) # G. C. Greubel, Dec 03 2024

Crossrefs

Cf. A154638, A169452, A170734.

Sequence in context: A165282 A165875 A166382 * A166971 A167116 A167671

Adjacent sequences: A166580 A166581 A166582 * A166584 A166585 A166586

Keyword

nonn

Author

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

Status

approved