cp's OEIS Frontend

A169570 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A169570 #8 Aug 08 2017 11:40:47
%S A169570 1,29,812,22736,636608,17825024,499100672,13974818816,391294926848,
%T A169570 10956257951744,306775222648832,8589706234167296,240511774556684288,
%U A169570 6734329687587160064,188561231252440481792,5279714475068333490176
%N A169570 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A169570 The initial terms coincide with those of A170748, although the two sequences are eventually different.
%C A169570 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169570 <a href="/index/Rec#order_35">Index entries for linear recurrences with constant coefficients</a>, signature (27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, -378).
%F A169570 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 A169570 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 A169570 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 A169570 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 A169570 + 2*t^2 + 2*t + 1)/(378*t^35 - 27*t^34 - 27*t^33 - 27*t^32 - 27*t^31 -
%F A169570 27*t^30 - 27*t^29 - 27*t^28 - 27*t^27 - 27*t^26 - 27*t^25 - 27*t^24 -
%F A169570 27*t^23 - 27*t^22 - 27*t^21 - 27*t^20 - 27*t^19 - 27*t^18 - 27*t^17 -
%F A169570 27*t^16 - 27*t^15 - 27*t^14 - 27*t^13 - 27*t^12 - 27*t^11 - 27*t^10 -
%F A169570 27*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 -
%F A169570 27*t + 1)
%t A169570 coxG[{35,378,-27}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 08 2017 *)
%K A169570 nonn
%O A169570 0,2
%A A169570 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009