  The problem of Hadamard quantum coin measurement in $n$ trials, with
arbitrary number of repeated consecutive last states is formulated in terms of
Fibonacci sequences for duplicated states, Tribonacci numbers for triplicated
states and $N$-Bonacci numbers for arbitrary $N$-plicated states. The
probability formulas for arbitrary position of repeated states are derived in
terms of Lucas and Fibonacci numbers. For generic qubit coin, the formulas are
expressed by Fibonacci and more general, $N$-Bonacci polynomials in qubit
probabilities. The generating function for probabilities, the Golden Ratio
limit of these probabilities and Shannon entropy for corresponding states are
determined. By generalized Born rule and universality of $n$-qubit measurement
gate, we formulate problem in terms of generic $n$-qubit states and construct
projection operators in Hilbert space, constrained on the Fibonacci tree of the
states. The results are generalized to qutrit and qudit coins, described by
generalized Fibonacci-$N$-Bonacci sequences.
