A177726 - OEIS

%I #2 Mar 30 2012 18:59:35

%S 0,0,0,0,0,0,0,0,0,22,52,90,136,190,252,322,400,486,620,770,936,1118,

%T 1316,1530,1760,2006,2268,2662,3088,3546,4036,4558,5112,5698,6316,

%U 6966,7800,8682,9612,10590,11616,12690,13812,14982,16200,17842,19564,21366

%N Number of line segments connecting exactly 10 points in an n x n grid of points

%C a(n) is also the number of pairs of points visible to each other exactly through 8 points in an n x n grid of points.

%H S. Mustonen, <a href="http://www.survo.fi/papers/LinesInGrid2.pdf">On lines going through a given number of points in a rectangular grid of points</a>

%F See Mathematica code.

%t j=9;

%t a[n_]:=a[n]=If[n<=j,0,2*a1[n]-a[n-1]+R1[n]]

%t a1[n_]:=a1[n]=If[n<=j,0,2*a[n-1]-a1[n-1]+R2[n]]

%t R1[n_]:=R1[n]=If[n<=j,0,R1[n-1]+4*S[n]]

%t R2[n_]:=(n-1)*S[n]

%t S[n_]:=If[Mod[n-1,j]==0,EulerPhi[(n-1)/j],0]

%t Table[a[n],{n,1,50}]

%K nonn

%O 1,10

%A _Seppo Mustonen_, May 13 2010