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A341474
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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.
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1
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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, 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, 10, 5, 21, 8, 19, 1, 17, 6, 19, 9, 10, 4, 17, 17, 6, 26, 13
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OFFSET
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0,6
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COMMENTS
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This sequence is a variant of A286327; here we consider tribonacci-like sequences, there Fibonacci like sequences. The scatterplots of these sequences are similar.
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LINKS
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FORMULA
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a(n) = 0 iff n = 0.
a(n) <= n^2.
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EXAMPLE
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The first terms of the elements t of T such that t(0)^2 + t(1)^2 + t(2)^2 <= 4 are:
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)
-------------------- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 1 2 4 7 13 24 44
1 0 1 0 1 2 3 6 11 20 37
1 1 0 0 1 1 2 4 7 13 24
2 0 1 1 2 4 7 13 24 44 81
2 1 0 1 2 3 6 11 20 37 68
2 1 1 0 2 3 5 10 18 33 61
3 1 1 1 3 5 9 17 31 57 105
4 0 0 2 2 4 8 14 26 48 88
4 0 2 0 2 4 6 12 22 40 74
4 2 0 0 2 2 4 8 14 26 48
- so a(0) = 0,
a(1) = a(2) = a(3) = a(4) = a(6) = a(7) = a(11) = 1,
a(5) = a(10) = a(18) = 2,
a(9) = a(17) = 3,
a(8) = a(12) = a(14) = 4.
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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