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A168780 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%I A168780 #18 Nov 24 2016 16:15:17
%S A168780 1,7,42,252,1512,9072,54432,326592,1959552,11757312,70543872,
%T A168780 423263232,2539579392,15237476352,91424858112,548549148672,
%U A168780 3291294892032,19747769352192,118486616113152,710919696678891,4265518180073220
%N A168780 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
%C A168780 The initial terms coincide with those of A003949, although the two sequences are eventually different.
%C A168780 First disagreement at index 19: a(19) = 710919696678891, A003949(19) = 710919696678912. - _Klaus Brockhaus_, Mar 25 2011
%C A168780 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168780 G. C. Greubel, <a href="/A168780/b168780.txt">Table of n, a(n) for n = 0..500</a>
%H A168780 <a href="/index/Rec#order_19">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, -15).
%F A168780 G.f.: (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^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 A168780 coxG[{19,15,-5}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 18 2015 *)
%t A168780 CoefficientList[Series[(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^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, 50}], t] (* _G. C. Greubel_, Aug 12 2016 *)
%Y A168780 Cf. A003949 (G.f.: (1+x)/(1-6*x)).
%K A168780 nonn,easy
%O A168780 0,2
%A A168780 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009