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A018809 Number of lines through exactly 2 points of an n X n grid of points. 5
0, 0, 6, 12, 48, 108, 248, 428, 764, 1196, 1900, 2668, 3824, 5244, 7248, 9380, 12192, 15372, 19528, 24020, 29732, 36052, 43808, 51836, 61636, 72492, 85308, 98492, 114012, 130668, 150196, 170828, 194768, 220276, 249452, 279284, 312572, 348036 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

S. Mustonen, On lines and their intersection points in a rectangular grid of points [From Seppo Mustonen, Apr 18 2009]

FORMULA

a(n) = (1/2) * (f(n, 3) - 2 f(n, 2) + f(n, 1)) where f(n, k) = Sum ((n - |kx|)(n - |ky|)); -n<kx<n, -n<ky<n, (x, y)=1. [Seppo Mustonen, Apr 18 2009]

MATHEMATICA

a[n_] := 1/2 (f[n, 3] - 2 f[n, 2] + f[n, 1]);

f[n_, k_] := Sum[x = kx/k; y = ky/k; If[IntegerQ[x] && IntegerQ[y] && CoprimeQ[x, y], (n - Abs[kx])(n - Abs[ky]), 0], {kx, -n + 1, n - 1}, {ky, -n + 1, n - 1}];

Table[a[n], {n, 0, 40}] (* Jean-Fran├žois Alcover, Oct 30 2018 *)

CROSSREFS

Sequence in context: A052904 A106692 A032470 * A226882 A214903 A256584

Adjacent sequences:  A018806 A018807 A018808 * A018810 A018811 A018812

KEYWORD

nonn

AUTHOR

David W. Wilson

EXTENSIONS

An incorrect formula removed by Seppo Mustonen, Apr 25 2009

STATUS

approved

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Last modified May 31 16:29 EDT 2020. Contains 334748 sequences. (Running on oeis4.)