The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A119437 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A119437

Table T(n,k) = number of lines through exactly k points of an n X n grid of points.
(history; published version)

#22 by N. J. A. Sloane at Fri Mar 13 19:51:19 EDT 2020

STATUS

editing

approved

#21 by N. J. A. Sloane at Fri Mar 13 19:51:17 EDT 2020

LINKS

Seppo Mustonen, <a href="/A018808/a018808.pdf">On lines and their intersection points in a rectangular grid of points</a> [Local copy]

STATUS

approved

editing

#20 by Michel Marcus at Mon Nov 27 03:19:22 EST 2017

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reviewed

approved

#19 by Joerg Arndt at Mon Nov 27 03:00:01 EST 2017

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proposed

reviewed

#18 by Jon E. Schoenfield at Sun Nov 26 15:03:22 EST 2017

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editing

proposed

#17 by Jon E. Schoenfield at Sun Nov 26 15:03:18 EST 2017

FORMULA

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|). [Seppo Mustonen, Apr 18 2009]

EXAMPLE

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proposed

editing

#16 by Wesley Ivan Hurt at Sun Nov 26 14:08:51 EST 2017

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editing

proposed

#15 by Wesley Ivan Hurt at Sun Nov 26 14:08:24 EST 2017

FORMULA

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_, Apr 18 2009]

STATUS

proposed

editing

#14 by Seiichi Manyama at Sun Nov 26 14:04:56 EST 2017

STATUS

editing

proposed

#13 by Seiichi Manyama at Sun Nov 26 14:01:19 EST 2017

EXAMPLE

From Seiichi Manyama, Nov 26 2017: (Start)

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8 | 764, 100, 44, 4, 4, 4, 18; (End)