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A170534 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.

%I A170534 #8 Feb 25 2024 19:10:00
%S A170534 1,45,1980,87120,3833280,168664320,7421230080,326534123520,
%T A170534 14367501434880,632170063134720,27815482777927680,1223881242228817920,
%U A170534 53850774658067988480,2369434084954991493120,104255099738019625697280
%N A170534 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
%C A170534 The initial terms coincide with those of A170764, although the two sequences are eventually different.
%C A170534 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170534 <a href="/index/Rec#order_46">Index entries for linear recurrences with constant coefficients</a>, signature (43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, -946).
%F A170534 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 A170534 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 A170534 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 A170534 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 A170534 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 A170534 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(946*t^46 - 43*t^45 -
%F A170534 43*t^44 - 43*t^43 - 43*t^42 - 43*t^41 - 43*t^40 - 43*t^39 - 43*t^38 -
%F A170534 43*t^37 - 43*t^36 - 43*t^35 - 43*t^34 - 43*t^33 - 43*t^32 - 43*t^31 -
%F A170534 43*t^30 - 43*t^29 - 43*t^28 - 43*t^27 - 43*t^26 - 43*t^25 - 43*t^24 -
%F A170534 43*t^23 - 43*t^22 - 43*t^21 - 43*t^20 - 43*t^19 - 43*t^18 - 43*t^17 -
%F A170534 43*t^16 - 43*t^15 - 43*t^14 - 43*t^13 - 43*t^12 - 43*t^11 - 43*t^10 -
%F A170534 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 -
%F A170534 43*t + 1)
%t A170534 coxG[{46,946,-43}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 25 2024 *)
%K A170534 nonn
%O A170534 0,2
%A A170534 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009