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nonn,look,new
Altug Alkan, <a href="/A296690/b296690.txt">Table of n, a(n) for n = 1..10000</a>
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a[n_] := a[n] = If[n<7, {2, 2, 2, 4, 5, 5}[[n]], a[n - a[n-1]] + a[n - a[n-2]] + a[n - a[n-3]]]; Array[a, 83100] (* after Giovanni Resta at A296440 *)