A177726 Number of line segments connecting exactly 10 points in an n x n grid of points

0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 52, 90, 136, 190, 252, 322, 400, 486, 620, 770, 936, 1118, 1316, 1530, 1760, 2006, 2268, 2662, 3088, 3546, 4036, 4558, 5112, 5698, 6316, 6966, 7800, 8682, 9612, 10590, 11616, 12690, 13812, 14982, 16200, 17842, 19564, 21366

Offset

1,10

Comments

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.

Links

Table of n, a(n) for n=1..48.

S. Mustonen, On lines going through a given number of points in a rectangular grid of points

Formula

See Mathematica code.

Mathematica

j=9;
a[n_]:=a[n]=If[n<=j, 0, 2*a1[n]-a[n-1]+R1[n]]
a1[n_]:=a1[n]=If[n<=j, 0, 2*a[n-1]-a1[n-1]+R2[n]]
R1[n_]:=R1[n]=If[n<=j, 0, R1[n-1]+4*S[n]]
R2[n_]:=(n-1)*S[n]
S[n_]:=If[Mod[n-1, j]==0, EulerPhi[(n-1)/j], 0]
Table[a[n], {n, 1, 50}]

Crossrefs

Sequence in context: A330409 A111576 A277979 * A101571 A290381 A324486

Adjacent sequences: A177723 A177724 A177725 * A177727 A177728 A177729

Keyword

nonn

Author

Seppo Mustonen, May 13 2010

Status

approved