A177721 Number of line segments connecting exactly 5 points in an n x n grid of points

0, 0, 0, 0, 12, 32, 60, 96, 160, 240, 336, 448, 632, 848, 1096, 1376, 1760, 2192, 2672, 3200, 3952, 4784, 5696, 6688, 7864, 9136, 10504, 11968, 13888, 15952, 18160, 20512, 23280, 26224, 29344, 32640, 36568, 40720, 45096, 49696, 54856, 60272, 65944

Offset

1,5

Comments

a(n) is also the number of pairs of points visible to each other exactly through 3 points in an n x n grid of points.

Links

Table of n, a(n) for n=1..43.

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

Seppo Mustonen, On lines going through a given number of points in a rectangular grid of points [Local copy]

Formula

See Mathematica code.

Mathematica

j=4;
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: A305074 A166959 A134582 * A081268 A332595 A188183

Adjacent sequences: A177718 A177719 A177720 * A177722 A177723 A177724

Keyword

nonn

Author

Seppo Mustonen, May 13 2010

Status

approved