A163743 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 42, 1722, 70602, 2894682, 118681101, 4865889840, 199500036960, 8179442209680, 335354699064000, 13749442969516380, 563723074403412000, 23112478470537775200, 947604746561778765600, 38851512911134346287200

Offset

0,2

Comments

The initial terms coincide with those of A170761, 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..615

Index entries for linear recurrences with constant coefficients, signature (40, 40, 40, 40, -820).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(820*t^5 - 40*t^4 - 40*t^3 - 40*t^2- 40*t + 1).

a(n) = 40*a(n-1)+40*a(n-2)+40*a(n-3)+40*a(n-4)-820*a(n-5). - Wesley Ivan Hurt, May 11 2021

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-41*x+860*x^5-820*x^6), {x, 0, 20}], x] (* G. C. Greubel, Aug 02 2017 *)
coxG[{5, 820, -40}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 24 2019 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-41*x+860*x^5-820*x^6)) \\ G. C. Greubel, Aug 02 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-41*x+860*x^5-820*x^6) )); // G. C. Greubel, May 24 2019
(Sage) ((1+x)*(1-x^5)/(1-41*x+860*x^5-820*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 24 2019

Crossrefs

Sequence in context: A120815 A162879 A163225 * A164112 A164686 A165174

Adjacent sequences: A163740 A163741 A163742 * A163744 A163745 A163746

Keyword

nonn

Author

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

Status

approved