cp's OEIS Frontend

A170185 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

%I A170185 #8 Nov 22 2016 15:57:02
%S A170185 1,32,992,30752,953312,29552672,916132832,28400117792,880403651552,
%T A170185 27292513198112,846067909141472,26228105183385632,813071260684954592,
%U A170185 25205209081233592352,781361481518241362912,24222205927065482250272
%N A170185 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
%C A170185 The initial terms coincide with those of A170751, although the two sequences are eventually different.
%C A170185 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170185 <a href="/index/Rec#order_39">Index entries for linear recurrences with constant coefficients</a>, signature (30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, -465).
%F A170185 G.f. (t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170185 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 +
%F A170185 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 +
%F A170185 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 +
%F A170185 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(465*t^39 -
%F A170185 30*t^38 - 30*t^37 - 30*t^36 - 30*t^35 - 30*t^34 - 30*t^33 - 30*t^32 -
%F A170185 30*t^31 - 30*t^30 - 30*t^29 - 30*t^28 - 30*t^27 - 30*t^26 - 30*t^25 -
%F A170185 30*t^24 - 30*t^23 - 30*t^22 - 30*t^21 - 30*t^20 - 30*t^19 - 30*t^18 -
%F A170185 30*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 -
%F A170185 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 -
%F A170185 30*t^2 - 30*t + 1)
%t A170185 coxG[{39,465,-30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 07 2016 *)
%K A170185 nonn
%O A170185 0,2
%A A170185 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009