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%I #13 Feb 14 2021 13:04:23
%S 0,1,1,1,1,2,1,1,2,3,2,1,2,1,2,3,3,3,2,3,1,3,2,4,1,3,2,3,4,3,5,3,4,2,
%T 4,3,4,1,4,3,2,5,4,5,1,5,3,5,2,5,3,5,4,3,6,5,6,3,6,4,3,2,6,4,3,5,4,7,
%U 1,7,4,7,3,4,2,7,5,4,6,5,4,1,8,5,4,3,5
%N Let T be the set of sequences {t(k), k >= 0} such that for any k >= 3, t(k) = t(k-1) + t(k-2) + t(k-3); a(n) is the least possible value of t(0) + t(1) + t(2) for an element t of T containing n.
%C This sequence is a variant of A249783; here we consider tribonacci-like sequences, there Fibonacci like sequences. The scatterplots of these sequences both present polygonal shapes emerging from the origin.
%H Rémy Sigrist, <a href="/A341456/b341456.txt">Table of n, a(n) for n = 0..10000</a>
%H Rémy Sigrist, <a href="/A341456/a341456.png">Scatterplot of the first 10000000 terms</a>
%H Rémy Sigrist, <a href="/A341456/a341456.gp.txt">PARI program for A341456</a>
%F a(n) = 0 iff n = 0.
%F a(n) = 1 iff n belongs to A213816.
%F a(n) <= n.
%e The first terms of the elements t of T such that t(0) + t(1) + t(2) <= 2 are:
%e t(0)+t(1)+t(2) t(0) t(1) t(2) t(3) t(4) t(5) t(6) t(7) t(8) t(9)
%e -------------- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
%e 0 0 0 0 0 0 0 0 0 0 0
%e 1 0 0 1 1 2 4 7 13 24 44
%e 1 0 1 0 1 2 3 6 11 20 37
%e 1 1 0 0 1 1 2 4 7 13 24
%e 2 0 0 2 2 4 8 14 26 48 88
%e 2 0 1 1 2 4 7 13 24 44 81
%e 2 0 2 0 2 4 6 12 22 40 74
%e 2 1 0 1 2 3 6 11 20 37 68
%e 2 1 1 0 2 3 5 10 18 33 61
%e 2 2 0 0 2 2 4 8 14 26 48
%e - so a(0) = 0,
%e a(1) = a(2) = a(3) = a(4) = a(6) = a(7) = a(11) = 1,
%e a(5) = = a(8) = a(10) = 2.
%o (PARI) See Links section.
%Y Cf. A000073, A001590, A213816, A249783.
%K nonn
%O 0,6
%A _Rémy Sigrist_, Feb 12 2021