cp's OEIS Frontend

A170313 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%I A170313 #6 Nov 22 2016 08:08:42
%S A170313 1,16,240,3600,54000,810000,12150000,182250000,2733750000,41006250000,
%T A170313 615093750000,9226406250000,138396093750000,2075941406250000,
%U A170313 31139121093750000,467086816406250000,7006302246093750000
%N A170313 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
%C A170313 The initial terms coincide with those of A170735, although the two sequences are eventually different.
%C A170313 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170313 <a href="/index/Rec#order_42">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, -105).
%F A170313 G.f. (t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170313 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A170313 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 A170313 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 A170313 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 A170313 2*t + 1)/(105*t^42 - 14*t^41 - 14*t^40 - 14*t^39 - 14*t^38 - 14*t^37 -
%F A170313 14*t^36 - 14*t^35 - 14*t^34 - 14*t^33 - 14*t^32 - 14*t^31 - 14*t^30 -
%F A170313 14*t^29 - 14*t^28 - 14*t^27 - 14*t^26 - 14*t^25 - 14*t^24 - 14*t^23 -
%F A170313 14*t^22 - 14*t^21 - 14*t^20 - 14*t^19 - 14*t^18 - 14*t^17 - 14*t^16 -
%F A170313 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 -
%F A170313 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1)
%K A170313 nonn
%O A170313 0,2
%A A170313 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009