cp's OEIS Frontend

A170025 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170025 #8 Jan 10 2017 18:13:48
%S A170025 1,16,240,3600,54000,810000,12150000,182250000,2733750000,41006250000,
%T A170025 615093750000,9226406250000,138396093750000,2075941406250000,
%U A170025 31139121093750000,467086816406250000,7006302246093750000
%N A170025 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170025 The initial terms coincide with those of A170735, although the two sequences are eventually different.
%C A170025 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170025 <a href="/index/Rec#order_36">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, -105).
%F A170025 G.f. (t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170025 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170025 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170025 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4
%F A170025 + 2*t^3 + 2*t^2 + 2*t + 1)/(105*t^36 - 14*t^35 - 14*t^34 - 14*t^33 -
%F A170025 14*t^32 - 14*t^31 - 14*t^30 - 14*t^29 - 14*t^28 - 14*t^27 - 14*t^26 -
%F A170025 14*t^25 - 14*t^24 - 14*t^23 - 14*t^22 - 14*t^21 - 14*t^20 - 14*t^19 -
%F A170025 14*t^18 - 14*t^17 - 14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 -
%F A170025 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4
%F A170025 - 14*t^3 - 14*t^2 - 14*t + 1)
%t A170025 coxG[{36,105,-14}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 10 2017 *)
%K A170025 nonn
%O A170025 0,2
%A A170025 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009