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`%I #19 Mar 04 2022 04:22:05
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`%S 1,0,1,0,2,0,1,3,0,1,0,2,0,4,0,1,0,2,0,1,3,0,1,0,5,0,1,0,2,0,1,3,0,1,
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`%T 0,2,0,4,0,1,0,2,0,1,6,0,1,0,2,0,1,3,0,1,0,2,0,4,0,1,0,2,0,1,3,0,1,0,
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`%U 5,0,1,0,2,0,1,3,0,1,0,2,0,7,0,1,0,2,0,1,3,0,1,0,2,0,4,0,1,0,2,0
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`%N Number of trailing 0's in tribonacci representation of n (cf. A278038).
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`%C The number mod 3 of trailing 0's in the tribonacci representation of n >= 1 (this sequence mod 3) is the tribonacci word itself (A080843). - _N. J. A. Sloane_, Oct 04 2018
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`%C The number of trailing 1's in the tribonacci representation of n >= 0 (cf. A278038) is also the tribonacci word itself (A080843).
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`%C From _Amiram Eldar_, Mar 04 2022: (Start)
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`%C The asymptotic density of the occurrences of k = 0, 1, 2, ... is (c-1)/c^(k+1), where c = 1.839286... (A058265) is the tribonacci constant.
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`%C The asymptotic mean of this sequence is 1/(c-1) = 1.191487... (End)
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`%H N. J. A. Sloane, <a href="/A278045/b278045.txt">Table of n, a(n) for n = 0..20000</a>
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`%t t[1] = 1; t[2] = 2; t[3] = 4; t[n_] := t[n] = t[n - 1] + t[n - 2] + t[n - 3]; a[0] = 1; a[n_] := Module[{s = {}, m = n, k}, While[m > 0, k = 1; While[t[k] <= m, k++]; k--; AppendTo[s, k]; m -= t[k]; k = 1]; Min[s] - 1]; Array[a, 100, 0] (* _Amiram Eldar_, Mar 04 2022 *)
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`%Y Cf. A278038, A278042, A278043, A278044, A080843, A058265.
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`%K nonn,base
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`%O 0,5
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`%A _N. J. A. Sloane_, Nov 18 2016
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