A163224 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 41, 1640, 65600, 2623180, 104894400, 4194464820, 167726145600, 6706948607580, 268194081870000, 10724409825744420, 428842296999090000, 17148329715447559980, 685718769084764781600, 27420176663127165184020

Offset

0,2

Comments

The initial terms coincide with those of A170760, 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..620

Index entries for linear recurrences with constant coefficients, signature (39,39,39,-780).

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(780*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).

a(n) = 39*a(n-1)+39*a(n-2)+39*a(n-3)-780*a(n-4). - Wesley Ivan Hurt, May 06 2021

Mathematica

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(780*t^4-39*t^3-39*t^2 - 39*t+1), {t, 0, 20}], t] (* or *) Join[{1}, LinearRecurrence[ {39, 39, 39, -780}, {41, 1640, 65600, 2623180} 20]] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, 780, -39}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 18 2019 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(780*t^4-39*t^3- 39*t^2-39*t+1)) \\ G. C. Greubel, Dec 11 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-40*x+819*x^4-780*x^5) )); // G. C. Greubel, Apr 30 2019
(Sage) ((1+x)*(1-x^4)/(1-40*x+819*x^4-780*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 2019

Crossrefs

Sequence in context: A180667 A281608 A162878 * A163677 A164091 A164685

Adjacent sequences: A163221 A163222 A163223 * A163225 A163226 A163227

Keyword

nonn

Author

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

Status

approved