A018812 - OEIS

%I #17 Nov 29 2017 09:22:35

%S 0,0,0,0,0,12,4,4,4,24,52,40,20,76,148,236,204,228,252,356,476,612,

%T 764,932,1116,1524,1548,1556,1548,1884,2252,2652,3084,3820,4620,5484,

%U 5524,6140,6788,7468,8180,8588,8996,9932,10916,12868,13820,14804,15820,17668

%N Number of lines through exactly 5 points of an n X n grid of points.

%H Seiichi Manyama, <a href="/A018812/b018812.txt">Table of n, a(n) for n = 0..1000</a>

%H S. Mustonen, <a href="http://www.survo.fi/papers/PointsInGrid.pdf">On lines and their intersection points in a rectangular grid of points</a> [From _Seppo Mustonen_, Apr 18 2009]

%F a(n) = 1/2 (f(n, 6) - 2 f(n, 5) + f(n, 4)) where f(n, k) = Sum ((n - |kx|)(n - |ky|)); -n<kx<n, -n<ky<n, (x, y)=1. [From _Seppo Mustonen_, Apr 18 2009]

%Y Cf. A119437.

%K nonn

%O 0,6

%A _David W. Wilson_