A162858 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

1, 38, 1406, 51319, 1872792, 68331600, 2493179658, 90967125816, 3319062151464, 121100596329852, 4418523599533920, 161215975658220768, 5882188976123487336, 214619841546851901024, 7830703259038738949472

Offset

0,2

Comments

The initial terms coincide with those of A170757, 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..638

Index entries for linear recurrences with constant coefficients, signature (36, 36, -666).

Formula

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(666*t^3 - 36*t^2 - 36*t + 1).

a(n) = 36*a(n-1) + 36*a(n-2) - 666*a(n-3), n > 0. - Muniru A Asiru, Oct 25 2018

G.f.: (1+x)*(1-x^3)/(1 - 37*x + 702*x^3 - 666*x^4). - G. C. Greubel, Apr 27 2019

Maple

seq(coeff(series((x^3+2*x^2+2*x+1)/(666*x^3-36*x^2-36*x+1), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 25 2018

Mathematica

CoefficientList[Series[(t^3+2*t^2+2*t+1)/(666*t^3-36*t^2-36*t+1), {t, 0, 20}], t] (* G. C. Greubel, Oct 24 2018 *)
coxG[{3, 666, -36}] (* 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)/(666*t^3-36*t^2-36*t+1)) \\ G. C. Greubel, Oct 24 2018
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!((t^3 + 2*t^2+2*t+1)/(666*t^3-36*t^2-36*t+1))); // G. C. Greubel, Oct 24 2018
(GAP) a:=[38, 1406, 51319];; for n in [4..20] do a[n]:=36*a[n-1]+36*a[n-2]-666*a[n-3]; od; Concatenation([1], a); # Muniru A Asiru, Oct 25 2018
(Sage) ((1+x)*(1-x^3)/(1 -37*x +702*x^3 -666*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019

Crossrefs

Sequence in context: A137030 A027657 A268885 * A163221 A163660 A164071

Adjacent sequences: A162855 A162856 A162857 * A162859 A162860 A162861

Keyword

nonn

Author

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

Status

approved