A165216 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 9, 72, 576, 4608, 36864, 294912, 2359296, 18874368, 150994908, 1207958976, 9663669540, 77309338176, 618474560256, 4947795320832, 39582353276928, 316658751897600, 2533269420638208, 20266150608766188, 162129166819422768

Offset

0,2

Comments

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

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

Links

Table of n, a(n) for n=0..19.

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

Formula

G.f. (t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +

1)/(28*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t

+ 1)

Mathematica

With[{num=Total[2t^Range[8]]+t^9+1, den=Total[-7 t^Range[8]]+ 28t^9+1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Oct 02 2011 *)

Crossrefs

Sequence in context: A163953 A164375 A164777 * A165787 A166367 A166541

Adjacent sequences: A165213 A165214 A165215 * A165217 A165218 A165219

Keyword

nonn

Author

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

Status

approved