Behaviour of $u_{n}=u_{\lfloor n/2\rfloor}+u_{\lfloor n/3\rfloor}+u_{\lfloor n/6\rfloor}$

See OEIS sequence A007731. This references a paper of P. Erdős, A. Hildebrand, A. Odlyzko, P. Pudaite and B. Reznick, The asymptotic behavior of a family of sequences, Pacific J. Math., 126 (1987), pp. 227-241, according to which the limit of $u_n/n$ is $12/\log(432)$.


Why don't you simply prove $\forall n\in\mathbb{N_+},\ u_n\leq3n$ by induction?

At least $u[1:6]$ satisfies this inequality.

Tags:

Recursion

Sequences And Series

Recurrence Relations

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