cp's OEIS Frontend

A170457 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.

%I A170457 #6 Nov 21 2016 16:50:00
%S A170457 1,16,240,3600,54000,810000,12150000,182250000,2733750000,41006250000,
%T A170457 615093750000,9226406250000,138396093750000,2075941406250000,
%U A170457 31139121093750000,467086816406250000,7006302246093750000
%N A170457 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
%C A170457 The initial terms coincide with those of A170735, although the two sequences are eventually different.
%C A170457 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170457 <a href="/index/Rec#order_45">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, 14, 14, 14, 14, 14, 14, -105).
%F A170457 G.f. (t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 +
%F A170457 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170457 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 +
%F A170457 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 +
%F A170457 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 +
%F A170457 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(105*t^45 - 14*t^44 - 14*t^43 -
%F A170457 14*t^42 - 14*t^41 - 14*t^40 - 14*t^39 - 14*t^38 - 14*t^37 - 14*t^36 -
%F A170457 14*t^35 - 14*t^34 - 14*t^33 - 14*t^32 - 14*t^31 - 14*t^30 - 14*t^29 -
%F A170457 14*t^28 - 14*t^27 - 14*t^26 - 14*t^25 - 14*t^24 - 14*t^23 - 14*t^22 -
%F A170457 14*t^21 - 14*t^20 - 14*t^19 - 14*t^18 - 14*t^17 - 14*t^16 - 14*t^15 -
%F A170457 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 -
%F A170457 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1)
%K A170457 nonn
%O A170457 0,2
%A A170457 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009