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%I #9 May 02 2019 15:43:45
%S 1,2,3,6,4,5,15,7,8,9,10,11,12,13,14,39,16,17,18,19,20,21,22,23,24,25,
%T 26,27,28,29,30,31,32,33,34,35,36,37,38,111,40,41,42,43,44,45,46,47,
%U 48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66
%N If the numbers a(1)...a(n) contain a hole, then a(n+1) is the smallest hole; otherwise a(n+1) = a(n-2) + a(n-1) + a(n).
%C This is to A060000 as tribonacci A000073 is to Fibonacci A000045. Let H be the set of positive numbers less than a(n) which are not equal to some a(i), i < n. This H is the 'set of holes so far'. If H is nonempty, then define a(n+1) = minimum(H). Otherwise define a(n+1) = a(n-2) + a(n-1) + a(n). Permutation of the natural numbers with inverse not yet in the OEIS.
%H Ivan Neretin, <a href="/A138153/b138153.txt">Table of n, a(n) for n = 1..10000</a>
%t a[n_] := a[n] = If[n < 4, n, Block[{s = Array[a, n-1]}, s = Complement[ Range[ Max@s], s]; If[s == {}, a[n - 1] + a[n - 2] + a[n - 3], First[s]]]]; Array[a, 80] (* _Giovanni Resta_, Jun 20 2016 *)
%Y Cf. A000040, A000073, A060000, A060013.
%K easy,nonn
%O 1,2
%A _Jonathan Vos Post_, May 04 2008
%E Data corrected by _Giovanni Resta_, Jun 20 2016
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