login
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

%I #11 Aug 21 2024 11:20:04

%S 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,

%T 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,

%U 12,9,15,8,13,10,17,13,12,8,18,14,11,12,10,17,6

%N 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}.

%H Rémy Sigrist, <a href="/A375479/b375479.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A375479/a375479.gp.txt">PARI program</a>

%e The first terms, alongside the corresponding slopes, are:

%e n a(n) Slopes

%e -- ---- -----------------------------------------------

%e 1 0 {}

%e 2 0 {}

%e 3 1 {0}

%e 4 2 {1/2, 1}

%e 5 1 {2/3}

%e 6 3 {-1, 1/4, 1/3}

%e 7 3 {3/5, 3/4, 2}

%e 8 0 {}

%e 9 5 {-3, -3/2, -1/2, -1/3, -1/5}

%e 10 3 {5/8, 5/7, 5}

%e 11 6 {-2, 1/6, 2/7, 3/8, 2/5, 3/2}

%e 12 3 {4/7, 5/6, 3}

%e 13 5 {-2/3, 1/8, 2/9, 3/11, 3/10}

%e 14 2 {5/12, 5/11}

%e 15 8 {-4/3, -3/5, -1/4, -1/7, -1/8, 1/11, 1/9, 2/13}

%o (PARI) \\ See Links section.

%Y Cf. A375480.

%K nonn

%O 1,4

%A _Rémy Sigrist_, Aug 17 2024