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A278778
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T(n,k)=Number of nXk 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly two mistakes.
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8
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0, 0, 0, 0, 2, 0, 1, 20, 20, 1, 6, 117, 266, 117, 6, 21, 503, 1972, 1972, 503, 21, 56, 1750, 10784, 19750, 10784, 1750, 56, 126, 5209, 48501, 150085, 150085, 48501, 5209, 126, 252, 13751, 189595, 955347, 1673658, 955347, 189595, 13751, 252, 462, 33000
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OFFSET
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1,5
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COMMENTS
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Table starts
...0.....0.......0.........1...........6............21..............56
...0.....2......20.......117.........503..........1750............5209
...0....20.....266......1972.......10784.........48501..........189595
...1...117....1972.....19750......150085........955347.........5355983
...6...503...10784....150085.....1673658......16205001.......141166787
..21..1750...48501....955347....16205001.....251740932......3634987413
..56..5209..189595...5355983...141166787....3634987413.....90752836672
.126.13751..665212..27218249..1126917480...48847405083...2155380363189
.252.33000.2138149.127644118..8340736743..611199661843..48042054699217
.462.73282.6384894.559023840.57745890265.7140933364136.999491681597761
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = (1/120)*n^5 - (1/24)*n^4 + (1/24)*n^3 + (1/24)*n^2 - (1/20)*n
k=2: [polynomial of degree 10]
k=3: [polynomial of degree 19]
k=4: [polynomial of degree 36]
k=5: [polynomial of degree 69]
k=6: [polynomial of degree 134]
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EXAMPLE
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Some solutions for n=4 k=4
..1..0..0..1. .1..1..0..0. .1..0..0..1. .1..1..1..1. .1..0..0..0
..1..1..0..1. .1..0..1..1. .1..1..0..0. .1..0..0..0. .0..1..0..1
..0..1..1..1. .0..1..1..1. .1..1..1..0. .0..1..1..0. .0..1..0..1
..0..1..1..1. .1..0..1..1. .0..0..1..0. .0..1..1..0. .1..0..0..1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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