cp's OEIS Frontend

A169509 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.

%I A169509 #8 Jan 13 2024 13:49:28
%S A169509 1,16,240,3600,54000,810000,12150000,182250000,2733750000,41006250000,
%T A169509 615093750000,9226406250000,138396093750000,2075941406250000,
%U A169509 31139121093750000,467086816406250000,7006302246093750000
%N A169509 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
%C A169509 The initial terms coincide with those of A170735, although the two sequences are eventually different.
%C A169509 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169509 <a href="/index/Rec#order_34">Index entries for linear recurrences with constant coefficients</a>, signature (14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, -105).
%F A169509 G.f. (t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A169509 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A169509 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A169509 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 +
%F A169509 2*t + 1)/(105*t^34 - 14*t^33 - 14*t^32 - 14*t^31 - 14*t^30 - 14*t^29 -
%F A169509 14*t^28 - 14*t^27 - 14*t^26 - 14*t^25 - 14*t^24 - 14*t^23 - 14*t^22 -
%F A169509 14*t^21 - 14*t^20 - 14*t^19 - 14*t^18 - 14*t^17 - 14*t^16 - 14*t^15 -
%F A169509 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 -
%F A169509 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1)
%t A169509 coxG[{34,105,-14}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 13 2024 *)
%K A169509 nonn
%O A169509 0,2
%A A169509 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009