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a(n) = floor((a(n-2)*a(n-1))/(a(n-1)+a(n-2))) + a(n-1) + a(n-2), a(0) = 0, a(1) = 1, a(2) = 1, ...
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%I #4 Mar 18 2013 16:42:22

%S 0,1,1,2,3,6,11,20,38,71,133,250,469,882,1657,3114,5852,10998,20669,

%T 38845,73004,137203,257857,484612,910773,1711693,3216930,6045851,

%U 11362482,21354481,40133296,75425924,141754368,266411067,500689027

%N a(n) = floor((a(n-2)*a(n-1))/(a(n-1)+a(n-2))) + a(n-1) + a(n-2), a(0) = 0, a(1) = 1, a(2) = 1, ...

%C lim n->inf a(n)/a(n-1) = 2*cos(Pi/9) = a root of 1 + 3*x - x^3

%t RecurrenceTable[{a[0]==0,a[1]==1,a[n]==Floor[(a[n-2]a[n-1])/(a[n-1]+a[n-2])]+ a[n-1]+a[n-2]},a,{n,40}] (* _Harvey P. Dale_, Mar 18 2013 *)

%K nonn

%O 0,4

%A _Gerald McGarvey_, Jul 21 2004