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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. 10
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,5
LINKS
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, ...
1, 6, 11, 18, 27, ...
1, 11, 20, 35, 52, ...
1, 18, 35, 62, 93, ...
1, 27, 52, 93, 140, ...
1, 38, 75, 136, 207, ...
MATHEMATICA
A[n_, k_] := (1/2)(f[n, k, 1] - f[n, k, 2]);
f[n_, k_, m_] := Sum[If[GCD[mx/m, my/m] == 1, (n - Abs[mx])(k - Abs[my]), 0], {mx, -n, n}, {my, -k, k}];
Table[A[n - k + 1, k], {n, 1, 11}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 04 2023 *)
CROSSREFS
Main diagonal gives A018808. Reading up to the diagonal gives A107348.
Sequence in context: A046617 A131063 A081579 * A146772 A202868 A202877
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Nov 26 2017
STATUS
approved

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Last modified May 30 00:40 EDT 2024. Contains 372954 sequences. (Running on oeis4.)