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A168683
Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
1
1, 6, 30, 150, 750, 3750, 18750, 93750, 468750, 2343750, 11718750, 58593750, 292968750, 1464843750, 7324218750, 36621093750, 183105468750, 915527343735, 4577636718600, 22888183592640, 114440917961400, 572204589798000
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003948, although the two sequences are eventually different.
First disagreement at index 17: a(17) = 915527343735, A003948(17) = 915527343750. - Klaus Brockhaus, Mar 30 2011
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,-10).
FORMULA
G.f.: (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) / (10*t^17 - 4*t^16 - 4*t^15 - 4*t^14 - 4*t^13 - 4*t^12 - 4*t^11 - 4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1).
G.f.: (1+t)*(1-t^17)/(1 -5*t +14*t^17 -10*t^18). - G. C. Greubel, Feb 22 2021
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^17)/(1 -5*t +14*t^17 -10*t^18), {t, 0, 40}], t] (* G. C. Greubel, Aug 03 2016, Feb 22 2021 *)
coxG[{17, 10, -4, 30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 09 2017 *)
PROG
(Magma)
R<t>:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( (1+t)*(1-t^17)/(1 -5*t +14*t^17 -10*t^18) )); // G. C. Greubel, Feb 22 2021
(Sage)
def A168683_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^17)/(1 -5*t +14*t^17 -10*t^18) ).list()
A168683_list(40) # G. C. Greubel, Feb 22 2021
CROSSREFS
Cf. A003948 (G.f.: (1+x)/(1-5*x)).
Sequence in context: A167107 A167651 A167897 * A168731 A168779 A168827
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved