A162871 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

1, 39, 1482, 55575, 2083692, 78111033, 2928135600, 109766289945, 4114781688966, 154249795892907, 5782323668697966, 216760526662519203, 8125647855742321632, 304604136609884440797, 11418619374984439210164

Offset

0,2

Comments

The initial terms coincide with those of A170758, 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 (37, 37, -703).

Formula

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(703*t^3 - 37*t^2 - 37*t + 1).

a(n) = 37*a(n-1) + 37*a(n-2) - 703*a(n-3), n > 0. - Muniru A Asiru, Oct 24 2018

G.f.: (1+x)*(1-x^3)/(1 - 38*x + 740*x^3 - 703*x^4). - G. C. Greubel, Apr 27 2019

Maple

seq(coeff(series((x^3+2*x^2+2*x+1)/(703*x^3-37*x^2-37*x+1), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 24 2018

Mathematica

coxG[{3, 703, -37}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 25 2018 *)
CoefficientList[Series[(t^3+2*t^2+2*t+1)/(703*t^3-37*t^2-37*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)/(703*t^3-37*t^2-37*t+1)) \\ G. C. Greubel, Oct 24 2018
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!((t^3 + 2*t^2+2*t+1)/(703*t^3-37*t^2-37*t+1))); // G. C. Greubel, Oct 24 2018
(GAP) a:=[39, 1482, 55575];; for n in [4..15] do a[n]:=37*a[n-1]+37*a[n-2]-703*a[n-3]; od; Concatenation([1], a); # Muniru A Asiru, Oct 24 2018
(Sage) ((1+x)*(1-x^3)/(1 -38*x +740*x^3 -703*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 27 2019

Crossrefs

Sequence in context: A020303 A235973 A097314 * A163222 A163668 A164084

Adjacent sequences: A162868 A162869 A162870 * A162872 A162873 A162874

Keyword

nonn

Author

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

Status

approved