A341474 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.
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
Offset: 0
Examples
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.
Links
- Rémy Sigrist, Table of n, a(n) for n = 0..10000
- Rémy Sigrist, Scatterplot of the first 100000 terms
- Rémy Sigrist, Scatterplot of the first 1000000 terms
- Rémy Sigrist, PARI program for A341474
Programs
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PARI
See Links section.
Comments