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A341456 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.

%I A341456 #13 Feb 14 2021 13:04:23
%S A341456 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 A341456 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 A341456 1,7,4,7,3,4,2,7,5,4,6,5,4,1,8,5,4,3,5
%N A341456 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 A341456 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 A341456 Rémy Sigrist, <a href="/A341456/b341456.txt">Table of n, a(n) for n = 0..10000</a>
%H A341456 Rémy Sigrist, <a href="/A341456/a341456.png">Scatterplot of the first 10000000 terms</a>
%H A341456 Rémy Sigrist, <a href="/A341456/a341456.gp.txt">PARI program for A341456</a>
%F A341456 a(n) = 0 iff n = 0.
%F A341456 a(n) = 1 iff n belongs to A213816.
%F A341456 a(n) <= n.
%e A341456 The first terms of the elements t of T such that t(0) + t(1) + t(2) <= 2 are:
%e A341456   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 A341456   --------------  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----
%e A341456                0     0     0     0     0     0     0     0     0     0     0
%e A341456                1     0     0     1     1     2     4     7    13    24    44
%e A341456                1     0     1     0     1     2     3     6    11    20    37
%e A341456                1     1     0     0     1     1     2     4     7    13    24
%e A341456                2     0     0     2     2     4     8    14    26    48    88
%e A341456                2     0     1     1     2     4     7    13    24    44    81
%e A341456                2     0     2     0     2     4     6    12    22    40    74
%e A341456                2     1     0     1     2     3     6    11    20    37    68
%e A341456                2     1     1     0     2     3     5    10    18    33    61
%e A341456                2     2     0     0     2     2     4     8    14    26    48
%e A341456 - so a(0) = 0,
%e A341456      a(1) = a(2) = a(3) = a(4) = a(6) = a(7) = a(11) = 1,
%e A341456      a(5) = = a(8) = a(10) = 2.
%o A341456 (PARI) See Links section.
%Y A341456 Cf. A000073, A001590, A213816, A249783.
%K A341456 nonn
%O A341456 0,6
%A A341456 _Rémy Sigrist_, Feb 12 2021