A163226 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 43, 1806, 75852, 3184881, 133727076, 5614945203, 235760834988, 9899147615406, 415646320207041, 17452195907135052, 732784406294332791, 30768219023291805678, 1291898809163525952060, 54244365975641552431917

Offset

0,2

Comments

The initial terms coincide with those of A170762, 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..610

Index entries for linear recurrences with constant coefficients, signature (41, 41, 41, -861).

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(861*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).

a(n) = 41*a(n-1)+41*a(n-2)+41*a(n-3)-861*a(n-4). - Wesley Ivan Hurt, May 06 2021

Mathematica

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(861*t^4-41*t^3-41*t^2 - 41*t+1), {t, 0, 20}], t] (* or *) Join[{1}, LinearRecurrence[ {41, 41, 41, -861}, {43, 1806, 75852, 3184881}, 20]] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, *61, -41}] (* 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)/(861*t^4-41*t^3 - 41*t^2-41*t+1)) \\ G. C. Greubel, Dec 11 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-42*x+902*x^4-861*x^5) )); // G. C. Greubel, Apr 30 2019
(Sage) ((1+x)*(1-x^4)/(1-42*x+902*x^4-861*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 2019

Crossrefs

Sequence in context: A297028 A198206 A162881 * A163745 A164113 A164687

Adjacent sequences: A163223 A163224 A163225 * A163227 A163228 A163229

Keyword

nonn

Author

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

Status

approved