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A170536 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.

%I A170536 #10 May 04 2021 15:54:39
%S A170536 1,47,2162,99452,4574792,210440432,9680259872,445291954112,
%T A170536 20483429889152,942237774900992,43342937645445632,1993775131690499072,
%U A170536 91713656057762957312,4218828178657096036352,194066096218226417672192
%N A170536 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
%C A170536 The initial terms coincide with those of A170766, although the two sequences are eventually different.
%C A170536 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170536 <a href="/index/Rec#order_46">Index entries for linear recurrences with constant coefficients</a>, signature (45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, -1035).
%F A170536 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 A170536 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 A170536 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 A170536 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 A170536 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 A170536 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1035*t^46 - 45*t^45 -
%F A170536 45*t^44 - 45*t^43 - 45*t^42 - 45*t^41 - 45*t^40 - 45*t^39 - 45*t^38 -
%F A170536 45*t^37 - 45*t^36 - 45*t^35 - 45*t^34 - 45*t^33 - 45*t^32 - 45*t^31 -
%F A170536 45*t^30 - 45*t^29 - 45*t^28 - 45*t^27 - 45*t^26 - 45*t^25 - 45*t^24 -
%F A170536 45*t^23 - 45*t^22 - 45*t^21 - 45*t^20 - 45*t^19 - 45*t^18 - 45*t^17 -
%F A170536 45*t^16 - 45*t^15 - 45*t^14 - 45*t^13 - 45*t^12 - 45*t^11 - 45*t^10 -
%F A170536 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 -
%F A170536 45*t + 1).
%F A170536 a(n) = -1035*a(n-46) + 45*Sum_{k=1..45} a(n-k). - _Wesley Ivan Hurt_, May 04 2021
%t A170536 coxG[{46,1035,-45}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 25 2015 *)
%K A170536 nonn
%O A170536 0,2
%A A170536 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009