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The set of integers for which the summands are distinct does not have a natural density but that the counting function oscillates in a predictable way (see ref)
Montgomery, Hugh, and Ulrike Vorhauer. <a href="https://www.ams.org/journals/mcom/2004-73-245/S0025-5718-03-01513-8/S0025-5718-03-01513-8.pdf">"Greedy sums of distinct squares."</a> Mathematics of computation 73.245 (2004): 493-513.
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The set of integers for which the summands are distinct does not have a natural density but that the counting function oscillates in a predictable way (see ref)
Montgomery, Hugh, and Ulrike Vorhauer. <a href="https://www.ams.org/journals/mcom/2004-73-245/S0025-5718-03-01513-8/S0025-5718-03-01513-8.pdf">"Greedy sums of distinct squares."</a> Mathematics of computation 73.245 (2004): 493-513.
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<a href="/index/Rec#order_02">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (2,-1).
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For n > 98, a(n) = n + 30. - Charles R Greathouse IV, Sep 02 2011 (This implies a(n+2) = 2*a(n+1)-a(n) for n > 98.)
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