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A141255
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Total number of line segments between points visible to each other in a square n X n lattice.
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2
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0, 6, 28, 86, 200, 418, 748, 1282, 2040, 3106, 4492, 6394, 8744, 11822, 15556, 20074, 25456, 32086, 39724, 48934, 59456, 71554, 85252, 101250, 119040, 139350, 161932, 187254, 215136, 246690, 280916, 319346, 361328, 407302, 457180, 511714, 570232
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A line segment joins points (a,b) and (c,d) if the points are distinct and gcd(c-a,d-b)=1.
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LINKS
| S. Mustonen, On lines going through a given number of points in a rectangular grid of points [From Seppo Mustonen (seppo.mustonen(AT)helsinki.fi), May 13 2010]
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FORMULA
| a(n) = A114043(n) - 1.
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EXAMPLE
| The 2 x 2 square lattice has a total of 6 line segments: 2 vertical, 2 horizonal and 2 diagonal.
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MATHEMATICA
| Table[cnt=0; Do[If[GCD[c-a, d-b]<2, cnt++ ], {a, n}, {b, n}, {c, n}, {d, n}]; (cnt-n^2)/2, {n, 20}]
Contribution from Seppo Mustonen (seppo.mustonen(AT)helsinki.fi), May 13 2010: (Start)
(* This recursive code is much more efficient. *)
a[n_]:=a[n]=If[n<=1, 0, 2*a1[n]-a[n-1]+R1[n]]
a1[n_]:=a1[n]=If[n<=1, 0, 2*a[n-1]-a1[n-1]+R2[n]]
R1[n_]:=R1[n]=If[n<=1, 0, R1[n-1]+4*EulerPhi[n-1]]
R2[n_]:=(n-1)*EulerPhi[n-1]
Table[a[n], {n, 1, 37}]
(End)
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CROSSREFS
| Cf. A141224.
Sequence in context: A144945 A202956 A055711 * A091321 A125310 A138874
Adjacent sequences: A141252 A141253 A141254 * A141256 A141257 A141258
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Jun 17 2008
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