cp's OEIS Frontend

A170265 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.

%I A170265 #8 Sep 04 2023 15:23:46
%S A170265 1,16,240,3600,54000,810000,12150000,182250000,2733750000,41006250000,
%T A170265 615093750000,9226406250000,138396093750000,2075941406250000,
%U A170265 31139121093750000,467086816406250000,7006302246093750000
%N A170265 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
%C A170265 The initial terms coincide with those of A170735, although the two sequences are eventually different.
%C A170265 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170265 <a href="/index/Rec#order_41">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, -105).
%F A170265 G.f. (t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170265 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A170265 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A170265 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A170265 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170265 1)/(105*t^41 - 14*t^40 - 14*t^39 - 14*t^38 - 14*t^37 - 14*t^36 - 14*t^35
%F A170265 - 14*t^34 - 14*t^33 - 14*t^32 - 14*t^31 - 14*t^30 - 14*t^29 - 14*t^28 -
%F A170265 14*t^27 - 14*t^26 - 14*t^25 - 14*t^24 - 14*t^23 - 14*t^22 - 14*t^21 -
%F A170265 14*t^20 - 14*t^19 - 14*t^18 - 14*t^17 - 14*t^16 - 14*t^15 - 14*t^14 -
%F A170265 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 -
%F A170265 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1)
%t A170265 coxG[{41,105,-14}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 04 2023 *)
%K A170265 nonn
%O A170265 0,2
%A A170265 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009