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A177725
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Number of line segments connecting exactly 9 points in an n x n grid of points
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0
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0, 0, 0, 0, 0, 0, 0, 0, 20, 48, 84, 128, 180, 240, 308, 384, 504, 640, 792, 960, 1144, 1344, 1560, 1792, 2144, 2528, 2944, 3392, 3872, 4384, 4928, 5504, 6248, 7040, 7880, 8768, 9704, 10688, 11720, 12800, 14264, 15808, 17432, 19136, 20920, 22784, 24728, 26752
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OFFSET
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1,9
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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 7 points in an n x n grid of points.
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LINKS
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FORMULA
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See Mathematica code.
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MATHEMATICA
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j=8;
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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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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