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A252889
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T(n,k)=Number of nXk nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 1 and every value increasing by 0 or 1 with every step right, diagonally se or down
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2
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0, 1, 1, 2, 1, 2, 3, 8, 8, 3, 4, 16, 18, 16, 4, 5, 24, 94, 94, 24, 5, 6, 32, 190, 386, 190, 32, 6, 7, 40, 290, 1729, 1729, 290, 40, 7, 8, 48, 390, 3577, 12200, 3577, 390, 48, 8, 9, 56, 490, 5600, 51496, 51496, 5600, 490, 56, 9, 10, 64, 590, 7648, 109736, 608993, 109736, 7648
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OFFSET
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1,4
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COMMENTS
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Table starts
.0..1...2.....3......4........5.........6...........7.............8
.1..1...8....16.....24.......32........40..........48............56
.2..8..18....94....190......290.......390.........490...........590
.3.16..94...386...1729.....3577......5600........7648..........9696
.4.24.190..1729..12200....51496....109736......176872........246312
.5.32.290..3577..51496...608993...2526480.....5560676.......9241012
.6.40.390..5600.109736..2526480..49489706...206094186.....468856938
.7.48.490..7648.176872..5560676.206094186..6648891794...28101900201
.8.56.590..9696.246312..9241012.468856938.28101900201.1489334202216
.9.64.690.11744.316008.13153668.803577258.66058900101.6425402265448
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = n - 1
k=2: a(n) = 8*n - 16 for n>2
k=3: a(n) = 100*n - 310 for n>4
k=4: a(n) = 2048*n - 8736 for n>6
k=5: a(n) = 69696*n - 380952 for n>8
k=6: a(n) = 3964928*n - 26499968 for n>10
k=7: a(n) = 378224704*n - 2991671254 for n>12
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..0..1....0..0..0..0....0..0..0..0....0..0..1..1....0..0..1..1
..1..1..1..1....0..0..0..1....0..0..1..1....0..1..1..2....0..0..1..2
..1..1..1..1....1..1..1..1....1..1..1..2....1..1..2..2....0..0..1..2
..1..1..2..2....1..1..1..2....1..1..1..2....2..2..2..2....0..0..1..2
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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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