

A119437


Table T(n,k) = number of lines through exactly k points of an n X n grid of points.


5



6, 12, 8, 48, 4, 10, 108, 16, 4, 12, 248, 36, 4, 4, 14, 428, 64, 20, 4, 4, 16, 764, 100, 44, 4, 4, 4, 18, 1196, 204, 36, 24, 4, 4, 4, 20, 1900, 252, 64, 52, 4, 4, 4, 4, 22, 2668, 396, 124, 40, 28, 4, 4, 4, 4, 24, 3824, 572, 200, 20, 60, 4, 4, 4, 4, 4, 26, 5244, 780, 236, 76, 44, 32
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OFFSET

2,1


LINKS



FORMULA

T(n,k) = 1/2 (f(n, k+1)  2 f(n, k) + f(n, k1)) where f(n, k) = Sum_{n < kx < n, n < ky < n, gcd(x, y)=1} (n  kx)*(n  ky). [Seppo Mustonen, Apr 18 2009]


EXAMPLE

The table starts:
n\k 2 3 4 5 6 7 8
+
2  6;
3  12, 8;
4  48, 4, 10;
5  108 16, 4, 12;
6  248, 36, 4, 4, 14;
7  428, 64, 20, 4, 4, 16;
8  764, 100, 44, 4, 4, 4, 18; (End)


CROSSREFS



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AUTHOR



EXTENSIONS



STATUS

approved



