cp's OEIS Frontend

A169202 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

%I A169202 #12 Oct 06 2020 17:20:02
%S A169202 1,45,1980,87120,3833280,168664320,7421230080,326534123520,
%T A169202 14367501434880,632170063134720,27815482777927680,1223881242228817920,
%U A169202 53850774658067988480,2369434084954991493120,104255099738019625697280
%N A169202 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
%C A169202 The initial terms coincide with those of A170764, although the two sequences are eventually different.
%C A169202 First disagreement at index 27: a(27) = 241536129364098218371082417239850527248874530, A170764(27) = 241536129364098218371082417239850527248875520. - _Klaus Brockhaus_, May 07 2011
%C A169202 Computed with Magma using commands similar to those used to compute A154638.
%H A169202 <a href="/index/Rec#order_27">Index entries for linear recurrences with constant coefficients</a>, signature (43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, -946).
%F A169202 G.f.: (t^27 + 2*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)/(946*t^27 - 43*t^26 - 43*t^25 - 43*t^24 - 43*t^23 - 43*t^22 - 43*t^21 - 43*t^20 - 43*t^19 - 43*t^18 - 43*t^17 - 43*t^16 - 43*t^15 - 43*t^14 - 43*t^13 - 43*t^12 - 43*t^11 - 43*t^10 - 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).
%t A169202 coxG[{27,946,-43}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 06 2020 *)
%Y A169202 Cf. A170764 (G.f.: (1+x)/(1-44*x)).
%K A169202 nonn
%O A169202 0,2
%A A169202 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009