A177723 Number of line segments connecting exactly 7 points in an n X n grid of points.

0, 0, 0, 0, 0, 0, 16, 40, 72, 112, 160, 216, 308, 416, 540, 680, 836, 1008, 1276, 1576, 1908, 2272, 2668, 3096, 3660, 4272, 4932, 5640, 6396, 7200, 8308, 9496, 10764, 12112, 13540, 15048, 16788, 18624, 20556, 22584, 24708, 26928, 29772, 32760

Offset

1,7

Comments

a(n) is also the number of pairs of points visible to each other exactly through 5 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=6;
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: A221684 A247345 A332519 * A174321 A258258 A086046

Adjacent sequences: A177720 A177721 A177722 * A177724 A177725 A177726

Keyword

nonn

Author

Seppo Mustonen, May 13 2010

Status

approved