A177720 Number of line segments connecting exactly 4 points in an n x n grid of points

0, 0, 0, 10, 28, 54, 104, 170, 252, 394, 568, 774, 1068, 1410, 1800, 2374, 3028, 3762, 4656, 5646, 6732, 8190, 9792, 11538, 13636, 15910, 18360, 21334, 24532, 27954, 31856, 36014, 40428, 45798, 51504, 57546, 64228, 71278, 78696, 87466, 96700

Offset

1,4

Comments

a(n) is also the number of pairs of points visible to each other exactly through 2 points in an n x n grid of points.

Links

Table of n, a(n) for n=1..41.

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=3;
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: A273195 A069953 A113746 * A117464 A081273 A060544

Adjacent sequences: A177717 A177718 A177719 * A177721 A177722 A177723

Keyword

nonn

Author

Seppo Mustonen, May 13 2010

Status

approved