A162755 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

1, 9, 72, 540, 4032, 29988, 223020, 1658160, 12328596, 91662732, 681510816, 5067014148, 37673118252, 280098623952, 2082525799284, 15483523651596, 115119584685504, 855911035979748, 6363675682412076, 47313758657548656, 351776531372292180, 2615449111101347724, 19445794254904116960

Offset

0,2

Comments

The initial terms coincide with those of A003951, although the two sequences are eventually different.

First disagreement at index 3: a(3) = 540, A003951(3) = 576. - Klaus Brockhaus, Jun 15 2011

Computed with Magma using commands similar to those used to compute A154638.

Links

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (7,7,-28).

Formula

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(28*t^3 - 7*t^2 - 7*t + 1)

a(0)=1, a(1)=9, a(2)=72, a(3)=540, a(n)=7*a(n-1)+7*a(n-2)-28*a(n-3). - Harvey P. Dale, Jun 15 2011

Mathematica

Join[{1}, LinearRecurrence[{7, 7, -28}, {9, 72, 540}, 50]] (* or *) CoefficientList[ Series[(t^3+2t^2+2t+1)/(28t^3-7t^2-7t+1), {t, 0, 50}], t] (* Harvey P. Dale, Jun 15 2011 *)

Crossrefs

Cf. A003951 (G.f.: (1+x)/(1-8*x)).

Sequence in context: A319892 A319873 A110396 * A045993 A084327 A057085

Adjacent sequences: A162752 A162753 A162754 * A162756 A162757 A162758

Keyword

nonn,easy,changed

Author

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

Status

approved