A166382 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 15, 210, 2940, 41160, 576240, 8067360, 112943040, 1581202560, 22136835840, 309915701760, 4338819824535, 60743477542020, 850408685567805, 11905721597662620, 166680102363263580, 2333521433029506720

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,-91).

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)/(91*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, Jul 23 2024: (Start)

a(n) = 13*Sum_{j=1..10} a(n-j) - 91*a(n-11).

G.f.: (1+x)*(1 - x^11)/(1 - 14*x + 104*x^11 - 91*x^12). (End)

Mathematica

With[{a=91, b=13}, CoefficientList[Series[(1+t)*(1-t^11)/(1-(b+1)*t +(a+b)*t^11-a*t^12), {t, 0, 40}], t]] (* G. C. Greubel, May 10 2016; Jul 23 2024 *)
coxG[{11, 91, -13}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 25 2019 *)

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-14*x+104*x^11-91*x^12) )); // G. C. Greubel, Jul 23 2024
(SageMath)
def A166382_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-14*x+104*x^11-91*x^12) ).list()
A166382_list(30) # G. C. Greubel, Jul 23 2024

Crossrefs

Cf. A154638, A169452, A170734.

Sequence in context: A164860 A165282 A165875 * A166583 A166971 A167116

Adjacent sequences: A166379 A166380 A166381 * A166383 A166384 A166385

Keyword

nonn

Author

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

Status

approved