A177722 Number of line segments connecting exactly 6 points in an n x n grid of points

0, 0, 0, 0, 0, 14, 36, 66, 104, 150, 228, 322, 432, 558, 700, 926, 1184, 1474, 1796, 2150, 2624, 3146, 3716, 4334, 5000, 5930, 6940, 8030, 9200, 10450, 11908, 13462, 15112, 16858, 18700, 21082, 23608, 26278, 29092, 32050, 35488, 39102, 42892, 46858

Offset

1,6

Comments

a(n) is also the number of pairs of points visible to each other exactly through 4 points in an n x n grid of points.

Links

Table of n, a(n) for n=1..44.

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

Formula

See Mathematica code.

Mathematica

j=5;
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: A024814 A340460 A268319 * A165761 A165765 A058486

Adjacent sequences: A177719 A177720 A177721 * A177723 A177724 A177725

Keyword

nonn

Author

Seppo Mustonen, May 13 2010

Status

approved