A167952 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

1, 36, 1260, 44100, 1543500, 54022500, 1890787500, 66177562500, 2316214687500, 81067514062500, 2837362992187500, 99307704726562500, 3475769665429687500, 121651938290039062500, 4257817840151367187500, 149023624405297851562500

Offset

0,2

Comments

The initial terms coincide with those of A170755, 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 (34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,-595).

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)/( 595*t^16 - 34*t^15 - 34*t^14 - 34*t^13 - 34*t^12 - 34*t^11 - 34*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).

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

G.f.: (1+t)*(1-t^16)/(1 - 35*t + 629*t^16 - 595*t^17).

a(n) = 34*Sum_{j=1..15} a(n-j) - 595*a(n-16). (End)

Mathematica

coxG[{16, 595, -34}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 07 2015 *)
CoefficientList[Series[(1+t)*(1-t^16)/(1-35*t+629*t^16-595*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 02 2016; Sep 06 2023 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-35*x+629*x^16-595*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)/(1-35*x+629*x^16-595*x^17) ).list()
A167955_list(40) # G. C. Greubel, Sep 06 2023

Crossrefs

Cf. A154638, A169452, A170755.

Sequence in context: A167429 A167815 A063819 * A168713 A168761 A168809

Adjacent sequences: A167949 A167950 A167951 * A167953 A167954 A167955

Keyword

nonn

Author

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

Status

approved