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A168754
Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
1
1, 29, 812, 22736, 636608, 17825024, 499100672, 13974818816, 391294926848, 10956257951744, 306775222648832, 8589706234167296, 240511774556684288, 6734329687587160064, 188561231252440481792, 5279714475068333490176
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170748, although the two sequences are eventually different.
First disagreement at index 18: a(18) = 115900292156700056776343146, A170748(18) = 115900292156700056776343552. - 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 (27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, -378).
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)/(378*t^18 - 27*t^17 - 27*t^16 - 27*t^15 - 27*t^14 - 27*t^13 - 27*t^12 - 27*t^11 - 27*t^10 - 27*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).
MATHEMATICA
With[{num=Total[2t^Range[17]]+t^18+1, den=Total[-27 t^Range[17]]+ 378t^18+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Feb 21 2013 *)
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)/(378*t^18 - 27*t^17 - 27*t^16 - 27*t^15 - 27*t^14 - 27*t^13 - 27*t^12 - 27*t^11 - 27*t^10 - 27*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 10 2016 *)
CROSSREFS
Cf. A170748 (G.f.: (1+x)/(1-28*x)).
Sequence in context: A167714 A167944 A168706 * A168802 A168850 A168898
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved