A177724 Number of line segments connecting exactly 8 points in an n x n grid of points

0, 0, 0, 0, 0, 0, 0, 18, 44, 78, 120, 170, 228, 294, 400, 522, 660, 814, 984, 1170, 1372, 1682, 2024, 2398, 2804, 3242, 3712, 4214, 4868, 5570, 6320, 7118, 7964, 8858, 9800, 11086, 12452, 13898, 15424, 17030, 18716, 20482, 22504, 24622, 26836, 29146

Offset

1,8

Comments

a(n) is also the number of pairs of points visible to each other exactly through 6 points in an n x n grid of points.

Links

Table of n, a(n) for n=1..46.

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

Formula

See Mathematica code.

Mathematica

j=7;
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: A049067 A114814 A299383 * A095739 A055577 A281917

Adjacent sequences: A177721 A177722 A177723 * A177725 A177726 A177727

Keyword

nonn

Author

Seppo Mustonen, May 13 2010

Status

approved