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A180980
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T(n,k) is the number of n X k binary matrices with floor((n*k)/2) 1's and rows in lexicographically nondecreasing order and columns in lexicographically nonincreasing order.
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1
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1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 3, 3, 1, 1, 3, 5, 5, 3, 1, 1, 4, 6, 8, 6, 4, 1, 1, 4, 8, 12, 12, 8, 4, 1, 1, 5, 10, 18, 20, 18, 10, 5, 1, 1, 5, 13, 24, 32, 32, 24, 13, 5, 1, 1, 6, 15, 33, 49, 58, 49, 33, 15, 6, 1, 1, 6, 18, 43, 73, 94, 94, 73, 43, 18, 6, 1, 1, 7, 21, 55, 102, 151, 169, 151, 102, 55, 21, 7, 1
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OFFSET
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1,5
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COMMENTS
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T(n,k) is the cardinality of a maximal antichain in the partially ordered set consisting of all k-tuples of natural numbers (x_1,...,x_k) with 0 < x_1 < ... < x_k < n+2, with the componentwise ordering, (x_1,...,x_k) <= (y_1,...,y_k) if and only if x_1 <= y_1, ..., x_k <= y_k. - Mamuka Jibladze, Nov 15 2020
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LINKS
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EXAMPLE
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Table starts:
1.1..1..1...1...1...1....1....1....1....1.....1.....1.....1.....1......1
1.2..2..3...3...4...4....5....5....6....6.....7.....7.....8.....8......9
1.2..3..5...6...8..10...13...15...18...21....25....28....32....36.....41
1.3..5..8..12..18..24...33...43...55...69....86...104...126...150....177
1.3..6.12..20..32..49...73..102..141..190...252...325...414...521....649
1.4..8.18..32..58..94..151..227..338..480...676...920..1242..1636...2137
1.4.10.24..49..94.169..289..468..734.1117..1656..2385..3370..4672...6375
1.5.13.33..73.151.289..526..910.1514.2430..3788..5744..8512.12346..17575
1.5.15.43.102.227.468..910.1667.2934.4968..8150.12954.20094.30441..45207
1.6.18.55.141.338.734.1514.2934.5448.9686.16660.27718.44916.70922.109583
All solutions for 3 X 4:
0..0..0..0....0..0..0..0....1..0..0..0....1..0..0..0....1..1..0..0
1..1..1..0....1..1..0..0....1..0..0..0....1..1..0..0....1..1..0..0
1..1..1..0....1..1..1..1....1..1..1..1....1..1..1..0....1..1..0..0
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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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