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A375479
For any n > 0, let S_n be the set of slopes of the straight lines passing through the points (i, a(i)) and (j, a(j)) for i < j <= n; a(1) = a(2) = 0, and then a(n) is the number of elements in S_{n-1} that are not is S_{n-2}.
2
0, 0, 1, 2, 1, 3, 3, 0, 5, 3, 6, 3, 5, 2, 8, 8, 5, 5, 4, 8, 7, 3, 12, 14, 11, 4, 14, 12, 5, 11, 7, 11, 9, 7, 14, 7, 11, 7, 14, 9, 8, 13, 7, 11, 8, 9, 10, 4, 21, 23, 19, 15, 9, 14, 9, 14, 13, 13, 12, 9, 15, 8, 13, 10, 17, 13, 12, 8, 18, 14, 11, 12, 10, 17, 6
OFFSET
1,4
LINKS
Rémy Sigrist, PARI program
EXAMPLE
The first terms, alongside the corresponding slopes, are:
n a(n) Slopes
-- ---- -----------------------------------------------
1 0 {}
2 0 {}
3 1 {0}
4 2 {1/2, 1}
5 1 {2/3}
6 3 {-1, 1/4, 1/3}
7 3 {3/5, 3/4, 2}
8 0 {}
9 5 {-3, -3/2, -1/2, -1/3, -1/5}
10 3 {5/8, 5/7, 5}
11 6 {-2, 1/6, 2/7, 3/8, 2/5, 3/2}
12 3 {4/7, 5/6, 3}
13 5 {-2/3, 1/8, 2/9, 3/11, 3/10}
14 2 {5/12, 5/11}
15 8 {-4/3, -3/5, -1/4, -1/7, -1/8, 1/11, 1/9, 2/13}
PROG
(PARI) \\ See Links section.
CROSSREFS
Cf. A375480.
Sequence in context: A144243 A125210 A098434 * A212634 A162883 A081446
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Aug 17 2024
STATUS
approved