cp's OEIS Frontend

A170004 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A170004 #8 Feb 28 2024 19:33:48
%S A170004 1,43,1806,75852,3185784,133802928,5619722976,236028364992,
%T A170004 9913191329664,416354035845888,17486869505527296,734448519232146432,
%U A170004 30846837807750150144,1295567187925506306048,54413821892871264854016
%N A170004 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A170004 The initial terms coincide with those of A170762, although the two sequences are eventually different.
%C A170004 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170004 <a href="/index/Rec#order_35">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, -861).
%F A170004 G.f. (t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A170004 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +
%F A170004 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +
%F A170004 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3
%F A170004 + 2*t^2 + 2*t + 1)/(861*t^35 - 41*t^34 - 41*t^33 - 41*t^32 - 41*t^31 -
%F A170004 41*t^30 - 41*t^29 - 41*t^28 - 41*t^27 - 41*t^26 - 41*t^25 - 41*t^24 -
%F A170004 41*t^23 - 41*t^22 - 41*t^21 - 41*t^20 - 41*t^19 - 41*t^18 - 41*t^17 -
%F A170004 41*t^16 - 41*t^15 - 41*t^14 - 41*t^13 - 41*t^12 - 41*t^11 - 41*t^10 -
%F A170004 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 -
%F A170004 41*t + 1)
%t A170004 coxG[{35,861,-41}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 28 2024 *)
%K A170004 nonn
%O A170004 0,2
%A A170004 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009