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A341456
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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) + t(1) + t(2) for an element t of T containing n.
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3
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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, 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, 1, 7, 4, 7, 3, 4, 2, 7, 5, 4, 6, 5, 4, 1, 8, 5, 4, 3, 5
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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 A249783; here we consider tribonacci-like sequences, there Fibonacci like sequences. The scatterplots of these sequences both present polygonal shapes emerging from the origin.
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LINKS
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FORMULA
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a(n) = 0 iff n = 0.
a(n) <= n.
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EXAMPLE
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The first terms of the elements t of T such that t(0) + t(1) + t(2) <= 2 are:
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)
-------------- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
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 0 2 2 4 8 14 26 48 88
2 0 1 1 2 4 7 13 24 44 81
2 0 2 0 2 4 6 12 22 40 74
2 1 0 1 2 3 6 11 20 37 68
2 1 1 0 2 3 5 10 18 33 61
2 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(8) = a(10) = 2.
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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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nonn
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AUTHOR
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STATUS
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approved
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