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 A227436 Triangle T(n, k) of the number of n X n binary matrices with k = 0..n^2 1's and no more than three 1's in the corners of any square sub-block. 1
 1, 1, 1, 4, 6, 4, 0, 1, 9, 36, 84, 121, 101, 38, 4, 0, 0, 1, 16, 120, 560, 1806, 4200, 7096, 8532, 6929, 3444, 876, 84, 2, 0, 0, 0, 0, 1, 25, 300, 2300, 12620, 52500, 170830, 441554, 910568, 1490996, 1912700, 1879432, 1368707 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Rows are of lengths 2, 5, 10, ..., i^2+1,.... Every row starts with k = 0. For all n: T(n, 0) = 1. The numbers are found by an exhaustive search among all (n^2, k)-combinations of 1's. Another description of the sequence: Given a square grid with side n and n^2 points, T(n,k) is the number of ways to choose k points of the grid, so that no 4 of the chosen points form a square with sides parallel to the grid. LINKS Heinrich Ludwig, Table of n, a(n) for n = 1..147 Heinrich Ludwig, CSV file for spreadsheets EXAMPLE T(n, k) written as a triangle 1,1; 1,4,6,4,0; 1,9,36,84,121,101,38,4,0,0; 1,16,120,560,1806,4200,7096,8532,6929,3444,876,84,2,0,0,0,0; ... For n = 4 there are 2 matrices with exactly k = 12 1's so that no more than three 1's are in the corners of any square sub-block. [0 1 1 1] [1 1 1 0] [1 1 0 1] [1 0 1 1] [1 0 1 1] [1 1 0 1] [1 1 1 0] [0 1 1 1] CROSSREFS Written T(n,k) as a triangle, column k = 1 gives the square numbers A000290, column k = 2 is A083374, column k = 3 is A178208. A227133(n) is the highest index k of a number greater than zero in the n-th row. Sequence in context: A123732 A244339 A253623 * A023901 A247669 A342278 Adjacent sequences: A227433 A227434 A227435 * A227437 A227438 A227439 KEYWORD tabf,nonn,hard AUTHOR Heinrich Ludwig, Jul 12 2013 STATUS approved

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Last modified March 1 17:48 EST 2024. Contains 370442 sequences. (Running on oeis4.)