A167951 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068154560, 1838317255040, 62502786671360, 2125094746826240, 72253221392092160, 2456609527331133440, 83524723929258536960, 2839840613594790256640, 96554580862222868725760

Offset

0,2

Comments

The initial terms coincide with those of A170754, 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 (33,33,33,33,33,33,33,33,33,33,33,33,33,33,33,-561).

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)/( 561*t^16 - 33*t^15 - 33*t^14 - 33*t^13 - 33*t^12 - 33*t^11 - 33*t^10 - 33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).

From G. C. Greubel, Sep 06 2023: (Start)

G.f.: (1+t)*(1-t^16)/(1 - 34*t + 594*t^16 - 561*t^17).

a(n) = 33*Sum_{j=1..15} a(n-j) - 561*a(n-16). (End)

Mathematica

CoefficientList[Series[(1+t)*(1-t^16)/(1-34*t+594*t^16-561*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 02 2016; Sep 06 2023 *)
coxG[{16, 561, -33}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 21 2017 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-34*x+594*x^16-561*x^17) )); // G. C. Greubel, Sep 06 2023
(SageMath)
def A167955_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-34*x+594*x^16-561*x^17) ).list()
A167955_list(40) # G. C. Greubel, Sep 06 2023

Crossrefs

Cf. A154638, A169452, A170754.

Sequence in context: A167088 A167405 A167789 * A168712 A168760 A168808

Adjacent sequences: A167948 A167949 A167950 * A167952 A167953 A167954

Keyword

nonn

Author

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

Status

approved