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%I #6 Mar 30 2012 18:49:45
%S 1,2,5,14,43,142,495,1794,6681,25346,97357,377038,1468019,5735758,
%T 22460935,88083586,345754097,1358000258,5335796565,20970349326,
%U 82429113339,324040664974,1273932845663,5008544929922,19691924052361
%N a(0)=1; a(1)=2; a(2)=5; a(3)=14; for n>3: a(n) = 8*a(n-1)-20*a(n-2)+16*a(n-3)-a(n-4).
%C a(n) is also the first entry of the vector M^n*[1,0,0,0], where M is the type F_4 Cartan matrix [[2,-1,0,0]; [ -1,2,-2,0]; [0,-1,2,-1]; [0,0,-1,2]].
%F G.f.: -(2*x-1)*(x^2-4*x+1)/(1-8*x+20*x^2-16*x^3+x^4). - _R. J. Mathar_, Nov 14 2007
%t a = {1,2,5,14}; Do[AppendTo[a, 8*a[[ -1]]-20*a[[ -2]]+16*a[[ -3]]-a[[ -4]]],{24}]; a
%Y Cf. A126569.
%K nonn
%O 0,2
%A _Gary W. Adamson_, Dec 28 2006
%E Edited and extended by _Stefan Steinerberger_, Aug 12 2007
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