cp's OEIS Frontend

A170169 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

%I A170169 #8 Sep 12 2017 12:13:04
%S A170169 1,16,240,3600,54000,810000,12150000,182250000,2733750000,41006250000,
%T A170169 615093750000,9226406250000,138396093750000,2075941406250000,
%U A170169 31139121093750000,467086816406250000,7006302246093750000
%N A170169 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
%C A170169 The initial terms coincide with those of A170735, although the two sequences are eventually different.
%C A170169 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170169 <a href="/index/Rec#order_39">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, 14, 14, 14, 14, 14, -105).
%F A170169 G.f. (t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170169 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 +
%F A170169 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 +
%F A170169 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 +
%F A170169 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(105*t^39 -
%F A170169 14*t^38 - 14*t^37 - 14*t^36 - 14*t^35 - 14*t^34 - 14*t^33 - 14*t^32 -
%F A170169 14*t^31 - 14*t^30 - 14*t^29 - 14*t^28 - 14*t^27 - 14*t^26 - 14*t^25 -
%F A170169 14*t^24 - 14*t^23 - 14*t^22 - 14*t^21 - 14*t^20 - 14*t^19 - 14*t^18 -
%F A170169 14*t^17 - 14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 -
%F A170169 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 -
%F A170169 14*t^2 - 14*t + 1)
%t A170169 coxG[{39,105,-14}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 12 2017 *)
%K A170169 nonn
%O A170169 0,2
%A A170169 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009