cp's OEIS Frontend

A169442 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169442 #15 May 08 2018 00:24:37
%S A169442 1,45,1980,87120,3833280,168664320,7421230080,326534123520,
%T A169442 14367501434880,632170063134720,27815482777927680,1223881242228817920,
%U A169442 53850774658067988480,2369434084954991493120,104255099738019625697280
%N A169442 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169442 The initial terms coincide with those of A170764, although the two sequences are eventually different.
%C A169442 First disagreement is at index 32, the difference is 990. - _Klaus Brockhaus_, Jun 30 2011
%C A169442 Computed with Magma using commands similar to those used to compute A154638.
%H A169442 <a href="/index/Rec#order_32">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, 43, 43, 43, 43, 43, -946).
%F A169442 G.f.: (t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*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^32 - 43*t^31 - 43*t^30 - 43*t^29 - 43*t^28 - 43*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).
%F A169442 G.f.: (1+2*sum(k=1..31,x^k)+x^32)/(1-43*sum(k=1..31,x^k)+946*x^32).
%Y A169442 Cf. A170764 (G.f.: (1+x)/(1-44*x) ).
%K A169442 nonn
%O A169442 0,2
%A A169442 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009