A162882 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

1, 44, 1892, 80410, 3416952, 145180728, 6168492330, 262088760780, 11135706433236, 473137249574682, 20102798001348216, 854133737629549608, 36290691560131770762, 1541929835910758016492, 65513979388697887768644

Offset

0,2

Comments

The initial terms coincide with those of A170763, 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..612

Index entries for linear recurrences with constant coefficients, signature (42, 42, -903).

Formula

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(903*t^3 - 42*t^2 - 42*t + 1).

a(n) = 42*a(n-1) + 42*a(n-2) - 903*a(n-3), n > 0. - Muniru A Asiru, Oct 24 2018

G.f.: (1+x)*(1-x^3)/(1 - 43*x + 945*x^3 - 903*x^4). - G. C. Greubel, Apr 27 2019

Maple

seq(coeff(series((x^3+2*x^2+2*x+1)/(903*x^3-42*x^2-42*x+1), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 24 2018

Mathematica

CoefficientList[Series[(t^3+2*t^2+2*t+1)/(903*t^3-42*t^2-42*t+1), {t, 0, 20}], t] (* G. C. Greubel, Oct 24 2018 *)
coxG[{3, 903, -42}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 27 2019 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((t^3+2*t^2+2*t+1)/(903*t^3-42*t^2-42*t+1)) \\ G. C. Greubel, Oct 24 2018
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!((t^3 + 2*t^2+2*t+1)/(903*t^3-42*t^2-42*t+1))); // G. C. Greubel, Oct 24 2018
(GAP) a:=[44, 1892, 80410];; for n in [4..20] do a[n]:=42*a[n-1]+42*a[n-2] -903*a[n-3]; od; Concatenation([1], a); # Muniru A Asiru, Oct 24 2018
(Sage) ((1+x)*(1-x^3)/(1 -43*x +945*x^3 -903*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 27 2019

Crossrefs

Sequence in context: A223049 A278793 A004295 * A163230 A163748 A164277

Adjacent sequences: A162879 A162880 A162881 * A162883 A162884 A162885

Keyword

nonn,easy

Author

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

Status

approved