cp's OEIS Frontend

A170601 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.

%I A170601 #8 Nov 21 2016 12:06:45
%S A170601 1,16,240,3600,54000,810000,12150000,182250000,2733750000,41006250000,
%T A170601 615093750000,9226406250000,138396093750000,2075941406250000,
%U A170601 31139121093750000,467086816406250000,7006302246093750000
%N A170601 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
%C A170601 The initial terms coincide with those of A170735, although the two sequences are eventually different.
%C A170601 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170601 <a href="/index/Rec#order_48">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, 14, 14, 14, -105).
%F A170601 G.f. (t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 +
%F A170601 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 +
%F A170601 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 +
%F A170601 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 +
%F A170601 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 +
%F A170601 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170601 1)/(105*t^48 - 14*t^47 - 14*t^46 - 14*t^45 - 14*t^44 - 14*t^43 - 14*t^42
%F A170601 - 14*t^41 - 14*t^40 - 14*t^39 - 14*t^38 - 14*t^37 - 14*t^36 - 14*t^35 -
%F A170601 14*t^34 - 14*t^33 - 14*t^32 - 14*t^31 - 14*t^30 - 14*t^29 - 14*t^28 -
%F A170601 14*t^27 - 14*t^26 - 14*t^25 - 14*t^24 - 14*t^23 - 14*t^22 - 14*t^21 -
%F A170601 14*t^20 - 14*t^19 - 14*t^18 - 14*t^17 - 14*t^16 - 14*t^15 - 14*t^14 -
%F A170601 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 -
%F A170601 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1)
%t A170601 coxG[{48,105,-14}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 06 2016 *)
%K A170601 nonn
%O A170601 0,2
%A A170601 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009