A167923 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

1, 15, 210, 2940, 41160, 576240, 8067360, 112943040, 1581202560, 22136835840, 309915701760, 4338819824640, 60743477544960, 850408685629440, 11905721598812160, 166680102383370240, 2333521433367183255

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 (13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,-91).

Formula

G.f.: (t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*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^16 - 13*t^15 - 13*t^14 - 13*t^13 - 13*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, Sep 10 2023: (Start)

G.f.: (1+t)*(1-t^16)/(1 - 14*t + 104*t^16 - 91*t^17).

a(n) = 13*Sum_{j=1..15} a(n-j) - 91*a(n-16). (End)

Mathematica

CoefficientList[Series[(1+t)*(1-t^16)/(1-14*t+104*t^16-91*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016; Sep 10 2023 *)
coxG[{16, 91, -13}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 22 2020 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-14*x+104*x^16-91*x^17) )); // G. C. Greubel, Sep 10 2023
(SageMath)
def A167955_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-14*x+104*x^16-91*x^17) ).list()
A167955_list(40) # G. C. Greubel, Sep 10 2023

Crossrefs

Cf. A154638, A169452, A170734.

Sequence in context: A166971 A167116 A167671 * A168692 A168740 A168788

Adjacent sequences: A167920 A167921 A167922 * A167924 A167925 A167926

Keyword

nonn

Author

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

Status

approved