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A177723 Number of line segments connecting exactly 7 points in an n X n grid of points. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 30 01:05 EDT 2022. Contains 357092 sequences. (Running on oeis4.)