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A168687 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%I A168687 #19 Mar 24 2021 08:05:53
%S A168687 1,10,90,810,7290,65610,590490,5314410,47829690,430467210,3874204890,
%T A168687 34867844010,313810596090,2824295364810,25418658283290,
%U A168687 228767924549610,2058911320946490,18530201888518365,166771816996664880
%N A168687 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
%C A168687 The initial terms coincide with those of A003952, although the two sequences are eventually different.
%C A168687 First disagreement at index 17: a(17) = 18530201888518365, A003952(17) = 18530201888518410. - _Klaus Brockhaus_, Mar 30 2011
%C A168687 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168687 G. C. Greubel, <a href="/A168687/b168687.txt">Table of n, a(n) for n = 0..500</a>
%H A168687 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,-36).
%F A168687 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)/ (36*t^17 - 8*t^16 - 8*t^15 - 8*t^14 - 8*t^13 - 8*t^12 - 8*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).
%F A168687 G.f.: (1+t)*(1-t^17)/(1 -9 *t + 44*t^17 - 36*t^18). - _G. C. Greubel_, Mar 24 2021
%t A168687 coxG[{17,36,-8}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 10 2015 *)
%t A168687 CoefficientList[Series[(1+t)*(1-t^17)/(1 -9*t +44*t^17 -36*t^18), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 03 2016; Mar 24 2021 *)
%o A168687 (Magma)
%o A168687 R<t>:=PowerSeriesRing(Integers(), 40);
%o A168687 Coefficients(R!( (1+t)*(1-t^17)/(1 -9*t +44*t^17 -36*t^18) )); // _G. C. Greubel_, Mar 24 2021
%o A168687 (Sage)
%o A168687 def A168687_list(prec):
%o A168687     P.<t> = PowerSeriesRing(ZZ, prec)
%o A168687     return P( (1+t)*(1-t^17)/(1 -9*t +44*t^17 -36*t^18) ).list()
%o A168687 A168687_list(40) # _G. C. Greubel_, Mar 24 2021
%Y A168687 Cf. A003952 (g.f.: (1+x)/(1-9*x)).
%K A168687 nonn
%O A168687 0,2
%A A168687 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009