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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.
0
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.
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 * A378483 A045993 A084327
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved