cp's OEIS Frontend

A170160 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

%I A170160 #8 Nov 22 2016 15:43:25
%S A170160 1,7,42,252,1512,9072,54432,326592,1959552,11757312,70543872,
%T A170160 423263232,2539579392,15237476352,91424858112,548549148672,
%U A170160 3291294892032,19747769352192,118486616113152,710919696678912,4265518180073472
%N A170160 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
%C A170160 The initial terms coincide with those of A003949, although the two sequences are eventually different.
%C A170160 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170160 <a href="/index/Rec#order_39">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, 5, 5, 5, 5, 5, 5, 5, 5, 5, -15).
%F A170160 G.f. (t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170160 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 +
%F A170160 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 +
%F A170160 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 +
%F A170160 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(15*t^39 -
%F A170160 5*t^38 - 5*t^37 - 5*t^36 - 5*t^35 - 5*t^34 - 5*t^33 - 5*t^32 - 5*t^31 -
%F A170160 5*t^30 - 5*t^29 - 5*t^28 - 5*t^27 - 5*t^26 - 5*t^25 - 5*t^24 - 5*t^23 -
%F A170160 5*t^22 - 5*t^21 - 5*t^20 - 5*t^19 - 5*t^18 - 5*t^17 - 5*t^16 - 5*t^15 -
%F A170160 5*t^14 - 5*t^13 - 5*t^12 - 5*t^11 - 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 -
%F A170160 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1)
%t A170160 coxG[{39,15,-5}] (* coxG program at A169452 *) (* _Harvey P. Dale_, Aug 18 2014 *)
%K A170160 nonn
%O A170160 0,2
%A A170160 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009