On a system of difference equations of third order solved in closed form
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Abstract
xn+1=(ayn-2xn-1yn+bxn-1yn-2+cyn-2+d)/(yn-2xn-1yn),
yn+1=(axn-2yn-1xn+byn-1xn-2+cxn-2+d)/(xn-2yn-1xn),
where n belongs to the set of positive integer numbers, x-2, x-1, x0, y-2, y-1 and y0 are arbitrary nonzero real numbers, and the parameters a, b, c and d are arbitrary real numbers with d nonzero can be solved in a closed form.
We will see that when a = b = c = d = 1, the solutions are expressed using the famous Tetranacci numbers. In particular, the results obtained here extend those in our recent work.
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