cp's OEIS Frontend

A169141 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

%I A169141 #10 Jan 02 2022 12:30:32
%S A169141 1,32,992,30752,953312,29552672,916132832,28400117792,880403651552,
%T A169141 27292513198112,846067909141472,26228105183385632,813071260684954592,
%U A169141 25205209081233592352,781361481518241362912,24222205927065482250272
%N A169141 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
%C A169141 The initial terms coincide with those of A170751, although the two sequences are eventually different.
%C A169141 First disagreement at index 26: a(26) = 615449359677803466682794047960571863536, A170751(26) = 615449359677803466682794047960571864032. - Klaus Brockhaus, Apr 30 2011
%C A169141 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169141 <a href="/index/Rec#order_26">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, -465).
%F A169141 G.f.: (t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 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 + 2*t + 1)/(465*t^26 - 30*t^25 - 30*t^24 - 30*t^23 - 30*t^22 - 30*t^21 - 30*t^20 - 30*t^19 - 30*t^18 - 30*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).
%t A169141 coxG[{26,465,-30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 02 2022 *)
%Y A169141 Cf. A170751 (G.f.: (1+x)/(1-31*x)).
%K A169141 nonn
%O A169141 0,2
%A A169141 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009