cp's OEIS Frontend

A169091 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.

%I A169091 #13 May 05 2020 15:32:55
%S A169091 1,30,870,25230,731670,21218430,615334470,17844699630,517496289270,
%T A169091 15007392388830,435214379276070,12621216999006030,366015292971174870,
%U A169091 10614443496164071230,307818861388758065670,8926746980273983904430
%N A169091 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
%C A169091 The initial terms coincide with those of A170749, although the two sequences are eventually different.
%C A169091 First disagreement at index 25: a(25) = 3755547024441991720544511984283789995, A170749(25) = 3755547024441991720544511984283790430. - Klaus Brockhaus, Apr 25 2011
%C A169091 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169091 Robert Israel, <a href="/A169091/b169091.txt">Table of n, a(n) for n = 0..683</a>
%H A169091 <a href="/index/Rec#order_25">Index entries for linear recurrences with constant coefficients</a>, signature (28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, -406).
%F A169091 G.f.: (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)/(406*t^25 - 28*t^24 - 28*t^23 - 28*t^22 - 28*t^21 - 28*t^20 - 28*t^19 - 28*t^18 - 28*t^17 - 28*t^16 - 28*t^15 - 28*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).
%t A169091 coxG[{25,406,-28}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 05 2015 *)
%Y A169091 Cf. A170749 (G.f.: (1+x)/(1-29*x)).
%K A169091 nonn
%O A169091 0,2
%A A169091 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009