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A168828 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

%I A168828 #14 Jan 12 2019 19:29:54
%S A168828 1,7,42,252,1512,9072,54432,326592,1959552,11757312,70543872,
%T A168828 423263232,2539579392,15237476352,91424858112,548549148672,
%U A168828 3291294892032,19747769352192,118486616113152,710919696678912,4265518180073451
%N A168828 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
%C A168828 The initial terms coincide with those of A003949, although the two sequences are eventually different.
%C A168828 First disagreement at index 20: a(20) = 4265518180073451, A003949(20) = 4265518180073472. - _Klaus Brockhaus_, Apr 01 2011
%C A168828 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168828 G. C. Greubel, <a href="/A168828/b168828.txt">Table of n, a(n) for n = 0..1000</a>
%H A168828 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, -15).
%F A168828 G.f.: (t^20 + 2*t^19 + 2*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)/(15*t^20 - 5*t^19 - 5*t^18 - 5*t^17 - 5*t^16 - 5*t^15 - 5*t^14 - 5*t^13 - 5*t^12 - 5*t^11 - 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).
%t A168828 CoefficientList[Series[(t^20 + 2*t^19 + 2*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)/(15*t^20 - 5*t^19 - 5*t^18 - 5*t^17 - 5*t^16 - 5*t^15 - 5*t^14 - 5*t^13 - 5*t^12 - 5*t^11 - 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1), {t,0,100}], t] (* _G. C. Greubel_, Nov 22 2016 *)
%t A168828 coxG[{20,15,-5}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 12 2019 *)
%Y A168828 Cf. A003949 (G.f.: (1+x)/(1-6*x)).
%K A168828 nonn
%O A168828 0,2
%A A168828 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009