cp's OEIS Frontend

A169306 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

%I A169306 #12 Mar 30 2025 14:29:03
%S A169306 1,5,20,80,320,1280,5120,20480,81920,327680,1310720,5242880,20971520,
%T A169306 83886080,335544320,1342177280,5368709120,21474836480,85899345920,
%U A169306 343597383680,1374389534720,5497558138880,21990232555520,87960930222080
%N A169306 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
%C A169306 The initial terms coincide with those of A003947, although the two sequences are eventually different.
%C A169306 First disagreement at index 30: a(30) = 1441151880758558710, A003947(30) = 1441151880758558720. - _Klaus Brockhaus_, Jun 22 2011
%C A169306 Computed with Magma using commands similar to those used to compute A154638.
%H A169306 <a href="/index/Rec#order_30">Index entries for linear recurrences with constant coefficients</a>, signature (3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -6).
%F A169306 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)/(6*t^30 - 3*t^29 - 3*t^28 - 3*t^27 - 3*t^26 - 3*t^25 - 3*t^24 - 3*t^23 - 3*t^22 - 3*t^21 - 3*t^20 - 3*t^19 - 3*t^18 - 3*t^17 - 3*t^16 - 3*t^15 - 3*t^14 - 3*t^13 - 3*t^12 - 3*t^11 - 3*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1).
%t A169306 coxG[{30,6,-3,30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Mar 30 2025 *)
%Y A169306 Cf. A003947 (G.f.: (1+x)/(1-4*x)).
%K A169306 nonn
%O A169306 0,2
%A A169306 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009