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A168772
Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
1
1, 47, 2162, 99452, 4574792, 210440432, 9680259872, 445291954112, 20483429889152, 942237774900992, 43342937645445632, 1993775131690499072, 91713656057762957312, 4218828178657096036352, 194066096218226417672192
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170766, although the two sequences are eventually different.
First disagreement at index 18: a(18) = 868922406908875183164862102471, A170766(18) = 868922406908875183164862103552. - Klaus Brockhaus, Mar 26 2011
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, -1035).
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)/(1035*t^18 - 45*t^17 - 45*t^16 - 45*t^15 - 45*t^14 - 45*t^13 - 45*t^12 - 45*t^11 - 45*t^10 - 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).
MATHEMATICA
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)/(1035*t^18 - 45*t^17 - 45*t^16 - 45*t^15 - 45*t^14 - 45*t^13 - 45*t^12 - 45*t^11 - 45*t^10 - 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 12 2016 *)
CROSSREFS
Cf. A170766 (G.f.: (1+x)/(1-46*x)).
Sequence in context: A167862 A167978 A168724 * A168820 A168868 A168916
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved