A167947 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513198112, 846067909141472, 26228105183385632, 813071260684954592, 25205209081233592352, 781361481518241362912, 24222205927065482250272

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170751, 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 (30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,-465).

Crossrefs

Cf. A154638, A169452, A170751.

Programs

Magma

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-31*x+495*x^16-465*x^17) )); // G. C. Greubel, Sep 07 2023

Mathematica

coxG[{16,465,-30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 16 2015 *)
CoefficientList[Series[(1+t)*(1-t^16)/(1-31*t+495*t^16-465*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 02 2016; Sep 07 2023 *)

SageMath

def A167947_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-31*x+495*x^16-465*x^17) ).list()
A167947_list(40) # G. C. Greubel, Sep 07 2023

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)/( 465*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).

From G. C. Greubel, Sep 07 2023: (Start)

G.f.: (1+t)*(1-t^16)/(1 - 31*t + 495*t^16 - 465*t^17).

a(n) = 30*Sum_{j=1..15} a(n-j) - 465*a(n-16). (End)