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A168743
Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
1
1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776946, 36287890208082, 616894133537394, 10487200270135698, 178282404592306866, 3030800878069216722, 51523614927176684274
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170737, although the two sequences are eventually different.
First disagreement at index 18: a(18) = 14890324713954061755033, A170737(18) = 14890324713954061755186. - Klaus Brockhaus, Mar 27 2011
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, -136).
FORMULA
G.f.: (t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*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)/(136*t^18 - 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).
MATHEMATICA
With[{num=Total[2t^Range[17]]+t^18+1, den=Total[-16 t^Range[17]]+ 136t^18+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Jan 04 2012 *)
CoefficientList[Series[(t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*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)/(136*t^18 - 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 10 2016 *)
CROSSREFS
Cf. A170737 (G.f.: (1+x)/(1-17*x)).
Sequence in context: A167674 A167927 A168695 * A168791 A168839 A168887
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved