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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 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, ... 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 Columns k=2..10 give A160842, A160843, A160844, A160845, A160846, A160847, A160848, A160849, A160850. Main diagonal gives A018808. Reading up to the diagonal gives A107348. Sequence in context: A046617 A131063 A081579 * A146772 A202868 A202877 Adjacent sequences: A295704 A295705 A295706 * A295708 A295709 A295710 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.)