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A177719
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Number of line segments connecting exactly 3 points in an n x n grid of points
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0
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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
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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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
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FORMULA
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See Mathematica code.
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MATHEMATICA
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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}]
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CROSSREFS
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Sequence in context: A159741 A099041 A129959 * A049724 A060602 A066605
Adjacent sequences: A177716 A177717 A177718 * A177720 A177721 A177722
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KEYWORD
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nonn
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AUTHOR
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Seppo Mustonen, May 13 2010
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STATUS
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approved
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