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A177719 Number of line segments connecting exactly 3 points in an n x n grid of points 0
0, 0, 8, 24, 60, 112, 212, 344, 548, 800, 1196, 1672, 2284, 2992, 3988, 5128, 6556, 8160, 10180, 12424, 15068, 17968, 21604, 25576, 30092, 34976, 40900, 47288, 54500, 62224, 70972, 80296, 90740, 101824, 114700, 128344, 143212, 158896, 176836 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

Mathematica code below computes with j=1 also A114043(n)-1 and A141255(n) much more efficiently than codes/formulas currently presented for those sequences.

LINKS

Table of n, a(n) for n=1..39.

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

FORMULA

See Mathematica code.

MATHEMATICA

j=2;

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: A159741 A099041 A129959 * A049724 A060602 A066605

Adjacent sequences:  A177716 A177717 A177718 * A177720 A177721 A177722

KEYWORD

nonn

AUTHOR

Seppo Mustonen, May 13 2010

STATUS

approved

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Last modified October 30 11:14 EDT 2014. Contains 248797 sequences.