cp's OEIS Frontend

A170233 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.

%I A170233 #8 Oct 10 2019 15:02:15
%S A170233 1,32,992,30752,953312,29552672,916132832,28400117792,880403651552,
%T A170233 27292513198112,846067909141472,26228105183385632,813071260684954592,
%U A170233 25205209081233592352,781361481518241362912,24222205927065482250272
%N A170233 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
%C A170233 The initial terms coincide with those of A170751, although the two sequences are eventually different.
%C A170233 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170233 <a href="/index/Rec#order_40">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, 30, -465).
%F A170233 G.f. (t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 +
%F A170233 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 A170233 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 A170233 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 A170233 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170233 1)/(465*t^40 - 30*t^39 - 30*t^38 - 30*t^37 - 30*t^36 - 30*t^35 - 30*t^34
%F A170233 - 30*t^33 - 30*t^32 - 30*t^31 - 30*t^30 - 30*t^29 - 30*t^28 - 30*t^27 -
%F A170233 30*t^26 - 30*t^25 - 30*t^24 - 30*t^23 - 30*t^22 - 30*t^21 - 30*t^20 -
%F A170233 30*t^19 - 30*t^18 - 30*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 -
%F A170233 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5
%F A170233 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1)
%t A170233 coxG[{40,465,-30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 10 2019 *)
%K A170233 nonn
%O A170233 0,2
%A A170233 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009