Fourth order linearly recurrent Wythoff pairs (Q1279857)

Let \(\phi\) be the golden ratio and \(a(n)=\lfloor n\phi\rfloor\), \(b(n)=\lfloor n\phi^2\rfloor\) where \(\lfloor\cdot\rfloor\) denotes the greatest integer function. A Wythoff triple is a triple \((i,a(i),b(i))\) where \(i{}\) is a positive integer (note that \(a(i)+i=b(i)\)). The author proves that there is an infinite sequence of Wythoff triples \((I_n,A_n,B_n)\) such that \(I_n,A_n\) and \(B_n\) all satisfy the irreducible linear recurrence \(C_{n+4}=10C_{n+3}- 16C_{n+2}+5C_{n+1}+C_n\).