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.
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
Offset: 0
Keywords
Examples
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.
Links
- Rémy Sigrist, Table of n, a(n) for n = 0..10000
- Rémy Sigrist, Scatterplot of the first 10000000 terms
- Rémy Sigrist, PARI program for A341456
Programs
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PARI
See Links section.
Comments