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A169308 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

%I A169308 #12 Apr 27 2019 11:37:09
%S A169308 1,7,42,252,1512,9072,54432,326592,1959552,11757312,70543872,
%T A169308 423263232,2539579392,15237476352,91424858112,548549148672,
%U A169308 3291294892032,19747769352192,118486616113152,710919696678912,4265518180073472
%N A169308 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
%C A169308 The initial terms coincide with those of A003949, although the two sequences are eventually different.
%C A169308 First disagreement at index 30: a(30) = 257919573007522250883051, A003949(30) = 257919573007522250883072. - _Klaus Brockhaus_, Jun 22 2011
%C A169308 Computed with Magma using commands similar to those used to compute A154638.
%H A169308 <a href="/index/Rec#order_30">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, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, -15).
%F A169308 G.f.: (t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*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^30 - 5*t^29 - 5*t^28 - 5*t^27 - 5*t^26 - 5*t^25 - 5*t^24 - 5*t^23 - 5*t^22 - 5*t^21 - 5*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 A169308 coxG[{30,15,-5}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 27 2019 *)
%Y A169308 Cf. A003949 (G.f.: (1+x)/(1-6*x)).
%K A169308 nonn
%O A169308 0,2
%A A169308 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009