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a(n) is the number of k > 0 such that n-1-2*k > 0 and the points (n-1-2*k, a(n-1-2*k)), (n-1-k, a(n-1-k)) and (n-1, a(n-1)) are aligned.
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%I #12 Jun 18 2019 11:58:09

%S 0,0,0,1,0,1,0,1,1,0,0,1,2,3,1,1,1,1,3,0,1,2,3,1,4,2,1,3,2,4,1,1,2,2,

%T 2,3,3,4,2,3,3,2,4,4,0,1,3,2,1,3,4,5,3,6,5,3,2,6,0,3,6,4,0,3,5,5,5,4,

%U 3,6,3,3,7,3,2,3,3,2,2,1,3,5,6,4,2,4,5

%N a(n) is the number of k > 0 such that n-1-2*k > 0 and the points (n-1-2*k, a(n-1-2*k)), (n-1-k, a(n-1-k)) and (n-1, a(n-1)) are aligned.

%C Is this sequence bounded?

%C Are there infinitely many null values?

%H Rémy Sigrist, <a href="/A308638/b308638.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A308638/a308638.png">Scatterplot of the first 25000000 terms</a>

%H Rémy Sigrist, <a href="/A308638/a308638.txt">C program for A308638</a>

%e The first terms, alongside the values of k such that (n-1-2*k, a(n-1-2*k)), (n-1-k, a(n-1-k)) and (n-1, a(n-1)), are:

%e n a(n) k's

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

%e 1 0 none

%e 2 0 none

%e 3 0 none

%e 4 1 1

%e 5 0 none

%e 6 1 2

%e 7 0 none

%e 8 1 2

%e 9 1 2

%e 10 0 none

%e 11 0 none

%e 12 1 4

%e 13 2 3,4

%e 14 3 1,4,5

%o (C) See Links section.

%Y See A308639 for a similar sequence.

%K nonn,look

%O 1,13

%A _Rémy Sigrist_, Jun 13 2019