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A170494 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.

%I A170494 #12 Oct 27 2019 12:42:27
%S A170494 1,5,20,80,320,1280,5120,20480,81920,327680,1310720,5242880,20971520,
%T A170494 83886080,335544320,1342177280,5368709120,21474836480,85899345920,
%U A170494 343597383680,1374389534720,5497558138880,21990232555520,87960930222080
%N A170494 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
%C A170494 The initial terms coincide with those of A003947, although the two sequences are eventually different.
%C A170494 First disagreement at index 46: a(46) = 6189700196426901374495621110, A003947(46) = 6189700196426901374495621120.
%C A170494 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170494 <a href="/index/Rec#order_46">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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -6).
%F A170494 G.f. (t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 +
%F A170494 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 +
%F A170494 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 +
%F A170494 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 +
%F A170494 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 +
%F A170494 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(6*t^46 - 3*t^45 -
%F A170494 3*t^44 - 3*t^43 - 3*t^42 - 3*t^41 - 3*t^40 - 3*t^39 - 3*t^38 - 3*t^37 -
%F A170494 3*t^36 - 3*t^35 - 3*t^34 - 3*t^33 - 3*t^32 - 3*t^31 - 3*t^30 - 3*t^29 -
%F A170494 3*t^28 - 3*t^27 - 3*t^26 - 3*t^25 - 3*t^24 - 3*t^23 - 3*t^22 - 3*t^21 -
%F A170494 3*t^20 - 3*t^19 - 3*t^18 - 3*t^17 - 3*t^16 - 3*t^15 - 3*t^14 - 3*t^13 -
%F A170494 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
%F A170494 - 3*t^3 - 3*t^2 - 3*t + 1)
%t A170494 coxG[{46,6,-3,30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 27 2019 *)
%Y A170494 A003947 (g.f.: (1+x)/(1-4*x)).
%K A170494 nonn
%O A170494 0,2
%A A170494 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009