A162877 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

1, 40, 1560, 60060, 2311920, 88979280, 3424561140, 131801403240, 5072652999960, 195231667516860, 7513899339838320, 289188142406526480, 11130010920731869140, 428361764988438838440, 16486399071025250766360

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..615

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

Formula

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

a(n) = 38*a(n-1) + 38*a(n-2) - 741*a(n-3), n > 0. - Muniru A Asiru, Oct 24 2018

G.f.: (1+x)*(1-x^3)/(1 - 39*x + 779*x^3 - 741*x^4). - G. C. Greubel, Apr 27 2019

Maple

seq(coeff(series((x^3+2*x^2+2*x+1)/(741*x^3-38*x^2-38*x+1), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 24 2018

Mathematica

coxG[{3, 741, -38}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 29 2017 *)
CoefficientList[Series[(t^3+2*t^2+2*t+1)/(741*t^3-38*t^2-38*t+1), {t, 0, 20}], t] (* G. C. Greubel, Oct 24 2018 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((t^3+2*t^2+2*t+1)/(741*t^3-38*t^2-38*t+1)) \\ G. C. Greubel, Oct 24 2018
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!((t^3 + 2*t^2+2*t+1)/(741*t^3-38*t^2-38*t+1))); // G. C. Greubel, Oct 24 2018
(GAP) a:=[40, 1560, 60060];; for n in [4..20] do a[n]:=38*a[n-1]+38*a[n-2] -741*a[n-3]; od; Concatenation([1], a); # Muniru A Asiru, Oct 24 2018
(Sage) ((1+x)*(1-x^3)/(1 -39*x +779*x^3 -741*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 27 2019

Crossrefs

Sequence in context: A049396 A135644 A165371 * A163223 A163669 A164085

Adjacent sequences: A162874 A162875 A162876 * A162878 A162879 A162880

Keyword

nonn

Author

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

Status

approved