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Proofs of some OEIS conjectures on Wythoff sums, Fibonacci and Lucas words
We prove several conjectures from the On-Line Encyclopedia of Integer Sequences about the lower and upper Wythoff sequences and the Fibonacci word. Among them are two of Kimberling's three conjectures on the number of ways to write $n=\lfloor hφ\rfloor+\lfloor kφ^2\rfloor$ with $h,k\ge1$ (A259598):
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