A295707 - OEIS

A295707

Square array A(n,k), n >= 1, k >= 1, read by antidiagonals, where A(n,k) is the number of lines through at least 2 points of an n X k grid of points.

0, 1, 1, 1, 6, 1, 1, 11, 11, 1, 1, 18, 20, 18, 1, 1, 27, 35, 35, 27, 1, 1, 38, 52, 62, 52, 38, 1, 1, 51, 75, 93, 93, 75, 51, 1, 1, 66, 100, 136, 140, 136, 100, 66, 1, 1, 83, 131, 181, 207, 207, 181, 131, 83, 1, 1, 102, 164, 238, 274, 306, 274, 238, 164, 102, 1

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OFFSET

1,5

LINKS

Seiichi Manyama, Antidiagonals n = 1..140, flattened

Seppo Mustonen, On lines and their intersection points in a rectangular grid of points

Seppo Mustonen, On lines and their intersection points in a rectangular grid of points [Local copy]

FORMULA

A(n,k) = (1/2) * (f(n,k,1) - f(n,k,2)), where f(n,k,m) = Sum ((n-|m*x|)*(k-|m*y|)); -n < m*x < n, -k < m*y < k, (x,y)=1.

EXAMPLE

Square array begins:

0, 1, 1, 1, 1, ...