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A201142
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T(n,k)=Number of nXk 0..5 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other
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8
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6, 15, 15, 20, 30, 20, 15, 5, 5, 15, 6, 135, 402, 135, 6, 1, 282, 117, 117, 282, 1, 6, 51, 5252, 7642, 5252, 51, 6, 15, 848, 758, 38763, 38763, 758, 848, 15, 20, 1189, 35810, 13009, 129244, 13009, 35810, 1189, 20, 15, 120, 4788, 593543, 120096, 120096
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OFFSET
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1,1
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COMMENTS
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Table starts
..6...15.....20.......15.........6..........1............6............15
.15...30......5......135.......282.........51..........848..........1189
.20....5....402......117......5252........758........35810..........4788
.15..135....117.....7642.....38763......13009.......593543.......2004404
..6..282...5252....38763....129244.....120096......4264060......46991775
..1...51....758....13009....120096....1268728......8360853......58395657
..6..848..35810...593543...4264060....8360853....543067656...11302225941
.15.1189...4788..2004404..46991775...58395657..11302225941..126701693572
.20..120.182640...480902.263910168..309819522.110916509158...83500574989
.15.2596..18486.17798640.769159517.1599103606.542120293937.9901442852486
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LINKS
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FORMULA
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T(n,1) = binomial(6,n modulo 6). For a 0..z array, T(n,1) = binomial(z+1, n modulo (z+1)).
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EXAMPLE
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Some solutions for n=3 k=7
..0..0..0..1..1..4..4....0..0..0..0..1..1..3....0..0..1..2..3..3..4
..0..2..2..3..3..4..5....1..2..2..2..3..3..5....0..1..2..3..4..4..4
..1..2..2..3..5..5..5....3..4..4..4..5..5..5....0..1..2..3..5..5..5
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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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