cp's OEIS Frontend

A170052 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170052 #8 Nov 26 2016 09:48:52
%S A170052 1,43,1806,75852,3185784,133802928,5619722976,236028364992,
%T A170052 9913191329664,416354035845888,17486869505527296,734448519232146432,
%U A170052 30846837807750150144,1295567187925506306048,54413821892871264854016
%N A170052 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170052 The initial terms coincide with those of A170762, although the two sequences are eventually different.
%C A170052 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170052 <a href="/index/Rec#order_36">Index entries for linear recurrences with constant coefficients</a>, signature (41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, -861).
%F A170052 G.f. (t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170052 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170052 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170052 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
%F A170052 + 2*t^3 + 2*t^2 + 2*t + 1)/(861*t^36 - 41*t^35 - 41*t^34 - 41*t^33 -
%F A170052 41*t^32 - 41*t^31 - 41*t^30 - 41*t^29 - 41*t^28 - 41*t^27 - 41*t^26 -
%F A170052 41*t^25 - 41*t^24 - 41*t^23 - 41*t^22 - 41*t^21 - 41*t^20 - 41*t^19 -
%F A170052 41*t^18 - 41*t^17 - 41*t^16 - 41*t^15 - 41*t^14 - 41*t^13 - 41*t^12 -
%F A170052 41*t^11 - 41*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4
%F A170052 - 41*t^3 - 41*t^2 - 41*t + 1)
%t A170052 coxG[{36,861,-41}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 17 2015 *)
%K A170052 nonn
%O A170052 0,2
%A A170052 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009