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%I #13 Feb 14 2021 14:49:27
%S 0,1,1,1,1,2,1,1,4,3,2,1,4,1,4,5,5,3,2,5,1,6,4,6,1,5,4,5,9,5,9,3,10,2,
%T 10,5,8,1,6,9,4,17,6,13,1,11,5,13,4,9,5,9,16,5,18,9,14,3,14,10,9,2,12,
%U 10,5,21,8,19,1,17,6,19,9,10,4,17,17,6,26,13
%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)^2 + t(1)^2 + t(2)^2 for an element t of T containing n.
%C This sequence is a variant of A286327; here we consider tribonacci-like sequences, there Fibonacci like sequences. The scatterplots of these sequences are similar.
%H Rémy Sigrist, <a href="/A341474/b341474.txt">Table of n, a(n) for n = 0..10000</a>
%H Rémy Sigrist, <a href="/A341474/a341474.png">Scatterplot of the first 100000 terms</a>
%H Rémy Sigrist, <a href="/A341474/a341474_1.png">Scatterplot of the first 1000000 terms</a>
%H Rémy Sigrist, <a href="/A341474/a341474.gp.txt">PARI program for A341474</a>
%F a(n) = 0 iff n = 0.
%F a(n) = 1 iff n belongs to A213816.
%F a(n) <= n^2.
%e The first terms of the elements t of T such that t(0)^2 + t(1)^2 + t(2)^2 <= 4 are:
%e t(0)^2+t(1)^2+t(3)^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 1 1 2 4 7 13 24 44 81
%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 3 1 1 1 3 5 9 17 31 57 105
%e 4 0 0 2 2 4 8 14 26 48 88
%e 4 0 2 0 2 4 6 12 22 40 74
%e 4 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(10) = a(18) = 2,
%e a(9) = a(17) = 3,
%e a(8) = a(12) = a(14) = 4.
%o (PARI) See Links section.
%Y Cf. A000073, A001590, A213816, A286327, A341456.
%K nonn,look
%O 0,6
%A _Rémy Sigrist_, Feb 13 2021