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Search: id:A141255
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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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+0
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; listen)
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OFFSET
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1,2
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COMMENT
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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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FORMULA
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a(n) = A114043(n) - 1.
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EXAMPLE
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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
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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}]
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CROSSREFS
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Cf. A141224.
Sequence in context: A119174 A144945 A055711 this_sequence A091321 A125310 A138874
Adjacent sequences: A141252 A141253 A141254 this_sequence A141256 A141257 A141258
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jun 17 2008
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