A177725 Number of line segments connecting exactly 9 points in an n x n grid of points

0, 0, 0, 0, 0, 0, 0, 0, 20, 48, 84, 128, 180, 240, 308, 384, 504, 640, 792, 960, 1144, 1344, 1560, 1792, 2144, 2528, 2944, 3392, 3872, 4384, 4928, 5504, 6248, 7040, 7880, 8768, 9704, 10688, 11720, 12800, 14264, 15808, 17432, 19136, 20920, 22784, 24728, 26752

Offset

1,9

Comments

a(n) is also the number of pairs of points visible to each other exactly through 7 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=8;
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: A234259 A135286 A338235 * A264444 A053245 A115882

Adjacent sequences: A177722 A177723 A177724 * A177726 A177727 A177728

Keyword

nonn

Author

Seppo Mustonen, May 13 2010

Status

approved