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Search: id:A119437
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| A119437 |
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Table T(n,k) = number of lines through exactly k points of an n X n grid of points. |
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+0
2
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| 6, 12, 8, 48, 4, 10, 108, 16, 4, 12, 248, 36, 4, 4, 14, 428, 64, 20, 4, 4, 16, 764, 100, 44, 4, 4, 4, 18, 1196, 204, 36, 24, 4, 4, 4, 20, 1900, 252, 64, 52, 4, 4, 4, 4, 22, 2668, 396, 124, 40, 28, 4, 4, 4, 4, 24, 3824, 572, 200, 20, 60, 4, 4, 4, 4, 4, 26, 5244, 780, 236, 76, 44, 32
(list; table; graph; listen)
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OFFSET
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2,1
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LINKS
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S. Mustonen, On lines and their intersection points in a rectangular grid of points [From Seppo Mustonen (seppo.mustonen(AT)helsinki.fi), Apr 18 2009]
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FORMULA
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T(n,k) = 1/2 (f(n, k+1) - 2 f(n, k) + f(n, k-1)) where f(n, k) = Sum_{-n<kx<n, -n<ky<n, gcd(x, y)=1} (n - |kx|)*(n - |ky|). [From Seppo Mustonen (seppo.mustonen(AT)helsinki.fi), Apr 18 2009]
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CROSSREFS
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Row sums A018808; columns A018809-A018817. See A119439 for another version.
Sequence in context: A028627 A162522 A028320 this_sequence A074474 A164378 A124349
Adjacent sequences: A119434 A119435 A119436 this_sequence A119438 A119439 A119440
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KEYWORD
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nonn,tabl
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 19 2006
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EXTENSIONS
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An incorrect formula removed by S. Mustonen (seppo.mustonen(AT)helsinki.fi), Apr 25 2009
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