A163223 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 40, 1560, 60840, 2371980, 92476800, 3605409600, 140564736000, 5480222014020, 213658376756760, 8329936604744040, 324760699264187160, 12661502336823753660, 493636212105145265520, 19245481572342746507280

Offset

0,2

Comments

The initial terms coincide with those of A170759, 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..625

Index entries for linear recurrences with constant coefficients, signature (38, 38, 38, -741).

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(741*t^4 - 38*t^3 - 38*t^2 - 38*t + 1).

a(n) = 38*a(n-1)+38*a(n-2)+38*a(n-3)-741*a(n-4). - Wesley Ivan Hurt, May 06 2021

Mathematica

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(741*t^4-38*t^3-38*t^2 - 38*t+1), {t, 0, 20}], t] (* or *) Join[{1}, LinearRecurrence[{38, 38, 38, -741}, {40, 1560, 60840, 2371980}, 20] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, 741, -38}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 30 2019 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(741*t^4- 38*t^3 -38*t^2-38*t+1)) \\ G. C. Greubel, Dec 11 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-39*x+779*x^4-741*x^5) )); // G. C. Greubel, Apr 30 2019
(Sage) ((1+x)*(1-x^4)/(1-39*x+779*x^4-741*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 2019

Crossrefs

Cf. A154638, A170759.

Sequence in context: A135644 A165371 A162877 * A163669 A164085 A164684

Adjacent sequences: A163220 A163221 A163222 * A163224 A163225 A163226

Keyword

nonn

Author

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

Status

approved