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 A266428 T(n,k)=Number of nXk binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing. 12
 2, 3, 3, 4, 7, 4, 5, 14, 13, 5, 6, 25, 39, 22, 6, 7, 41, 106, 96, 34, 7, 8, 63, 259, 404, 212, 50, 8, 9, 92, 574, 1556, 1391, 433, 70, 9, 10, 129, 1170, 5365, 8764, 4383, 826, 95, 10, 11, 175, 2223, 16585, 49894, 45907, 12758, 1493, 125, 11, 12, 231, 3982, 46463, 251381 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ..2...3....4......5........6..........7............8............9 ..3...7...14.....25.......41.........63...........92..........129 ..4..13...39....106......259........574.........1170.........2223 ..5..22...96....404.....1556.......5365........16585........46463 ..6..34..212...1391.....8764......49894.......251381......1122721 ..7..50..433...4383....45907.....448649......3889553.....29520031 ..8..70..826..12758...223075....3825307.....59155748....798834778 ..9..95.1493..34611..1005991...30555624....861030491..21325003746 .10.125.2575..88206..4224203..227542455..11809616668.546283341439 .11.161.4270.212609.16588684.1579153474.151566391972 LINKS R. H. Hardin, Table of n, a(n) for n = 1..145 FORMULA Empirical for column k: k=1: a(n) = 2*a(n-1) -a(n-2) k=2: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5) k=3: [order 12] Empirical for row n: n=1: a(n) = n + 1 n=2: a(n) = (1/6)*n^3 + (1/2)*n^2 + (4/3)*n + 1 n=3: [polynomial of degree 6] n=4: [polynomial of degree 11] n=5: [polynomial of degree 19] n=6: [polynomial of degree 33] n=7: [polynomial of degree 57] EXAMPLE Some solutions for n=4 k=4 ..0..0..0..0....0..0..1..1....0..0..0..1....0..0..1..1....0..0..0..1 ..0..0..0..1....0..0..1..1....0..0..1..0....0..1..0..1....0..1..1..1 ..0..0..1..1....1..1..0..1....0..1..1..1....0..1..1..1....0..1..1..1 ..0..1..0..1....1..1..1..0....1..1..0..0....1..1..1..0....1..0..0..1 CROSSREFS Column 1 and row 1 are A000027(n+1). Column 2 is A002623. Row 2 is A004006(n+1). Sequence in context: A227125 A248944 A267245 * A180985 A227385 A049790 Adjacent sequences: A266425 A266426 A266427 * A266429 A266430 A266431 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Dec 29 2015 STATUS approved

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Last modified December 9 18:33 EST 2023. Contains 367693 sequences. (Running on oeis4.)