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A252938
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T(n,k)=Number of nXk nonnegative integer arrays with upper left 0 and every value within 3 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down
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8
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1, 2, 2, 4, 5, 4, 8, 13, 13, 8, 15, 34, 44, 34, 15, 26, 83, 153, 153, 83, 26, 42, 176, 494, 711, 494, 176, 42, 64, 329, 1343, 3067, 3067, 1343, 329, 64, 93, 558, 3016, 10920, 17962, 10920, 3016, 558, 93, 130, 879, 5833, 30818, 86488, 86488, 30818, 5833, 879, 130, 176
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OFFSET
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1,2
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COMMENTS
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Table starts
...1....2.....4......8......15.......26.........42..........64...........93
...2....5....13.....34......83......176........329.........558..........879
...4...13....44....153.....494.....1343.......3016........5833........10114
...8...34...153....711....3067....10920......30818.......70640.......138558
..15...83...494...3067...17962....86488.....320270......917811......2127013
..26..176..1343..10920...86488...578342....2952734....11219797.....32649081
..42..329..3016..30818..320270..2952734...21312696...113154831....440052087
..64..558..5833..70640..917811.11219797..113154831...857248091...4687944300
..93..879.10114.138558.2127013.32649081..440052087..4687944300..36723156004
.130.1308.16179.242764.4211511.76641323.1302939451.18615501830.205553855458
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = (1/6)*n^3 - (1/2)*n^2 + (4/3)*n
k=2: a(n) = (8/3)*n^3 - 18*n^2 + (145/3)*n - 42 for n>2
k=3: a(n) = (160/3)*n^3 - 548*n^2 + (6071/3)*n - 2591 for n>4
k=4: a(n) = (4096/3)*n^3 - 18720*n^2 + (269642/3)*n - 149376 for n>6
k=5: a(n) = (133120/3)*n^3 - 760496*n^2 + (13526246/3)*n - 9199709 for n>8
k=6: [polynomial of degree 3] for n>10
k=7: [polynomial of degree 3] for n>12
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..1..2....0..0..1..1....0..1..1..2....0..1..1..1....0..0..0..1
..0..0..1..2....1..1..1..1....0..1..2..2....0..1..2..2....1..1..1..1
..1..1..1..2....1..2..2..2....1..1..2..2....0..1..2..2....1..2..2..2
..1..2..2..2....2..2..2..3....1..2..2..2....1..1..2..3....2..2..2..3
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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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