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We compute exactly the distribution of the occupation time in a discrete non-Markovian toy sequence which appears in various physical contexts such as the diffusion processes and Ising spin glass chains. The non-Markovian property makes the results nontrivial even for this toy sequence. The distribution is shown to have non-Gaussian tails characterized by a nontrivial large deviation function which is computed explicitly. An exact mapping of this sequence to an Ising spin glass chain via adoi:10.1103/physreve.66.041102 pmid:12443172 fatcat:mmt4bcmdtrdejd3y434izi7tsy