

A334044


a(1) = 0, and for any n > 1, a(n) is the number of points of the set { (k, a(k)), k = 1..n2 } that are not visible from the point (n1, a(n1)).


2



0, 0, 0, 1, 0, 2, 1, 0, 4, 1, 1, 2, 2, 2, 3, 2, 3, 5, 2, 6, 4, 3, 3, 4, 4, 7, 1, 5, 5, 2, 6, 5, 4, 6, 6, 9, 0, 6, 9, 3, 4, 7, 5, 8, 5, 6, 6, 10, 8, 10, 7, 7, 7, 5, 6, 11, 6, 11, 8, 6, 14, 8, 8, 10, 11, 9, 8, 15, 8, 12, 8, 12, 11, 6, 14, 8, 12, 14, 10, 13, 8
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,6


COMMENTS

For any i and k such that i < k: the point (i, a(i)) is visible from the point (k, a(k)) if there are no j such that i < j < k and the three points (i, a(i)), (j, a(j)), (k, a(k)) are aligned.


LINKS



EXAMPLE

For n = 6:
 we consider the following points:
. . . X .
(4,1)
X X X . X
(1,0) (2,0) (3,0) (5,0)
 the points (1,0) and (2,0) are not visible from (5,0)
(as they are hidden by (3,0)),
 whereas the points (3,0) and (4,1) are visible from (5,0)
 hence a(6) = 2.


PROG

(PARI) g(z) = z/gcd(real(z), imag(z))
for (n=1, #a=vector(81), print1 (a[n] = max(0, n2)  #Set(apply(k > g((k+a[k]*I)(n1+a[n1]*I)), [1..n2]))", "))


CROSSREFS

See A334043 for a similar sequence.


KEYWORD

nonn


AUTHOR



STATUS

approved



