cp's OEIS Frontend

A170100 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

%I A170100 #6 Nov 26 2016 10:11:56
%S A170100 1,43,1806,75852,3185784,133802928,5619722976,236028364992,
%T A170100 9913191329664,416354035845888,17486869505527296,734448519232146432,
%U A170100 30846837807750150144,1295567187925506306048,54413821892871264854016
%N A170100 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
%C A170100 The initial terms coincide with those of A170762, although the two sequences are eventually different.
%C A170100 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170100 <a href="/index/Rec#order_37">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, 41, -861).
%F A170100 G.f. (t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170100 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 +
%F A170100 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 +
%F A170100 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 +
%F A170100 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(861*t^37 - 41*t^36 - 41*t^35 -
%F A170100 41*t^34 - 41*t^33 - 41*t^32 - 41*t^31 - 41*t^30 - 41*t^29 - 41*t^28 -
%F A170100 41*t^27 - 41*t^26 - 41*t^25 - 41*t^24 - 41*t^23 - 41*t^22 - 41*t^21 -
%F A170100 41*t^20 - 41*t^19 - 41*t^18 - 41*t^17 - 41*t^16 - 41*t^15 - 41*t^14 -
%F A170100 41*t^13 - 41*t^12 - 41*t^11 - 41*t^10 - 41*t^9 - 41*t^8 - 41*t^7 -
%F A170100 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1)
%K A170100 nonn
%O A170100 0,2
%A A170100 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009