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A252828
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T(n,k)=Number of nXk nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down
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8
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1, 2, 2, 4, 6, 4, 8, 18, 18, 8, 15, 53, 81, 53, 15, 26, 142, 340, 340, 142, 26, 42, 339, 1238, 1920, 1238, 339, 42, 64, 729, 3891, 9075, 9075, 3891, 729, 64, 93, 1437, 10761, 36292, 54376, 36292, 10761, 1437, 93, 130, 2638, 26764, 125892, 271846, 271846, 125892
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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....6.....18......53......142.......339........729........1437.........2638
...4...18.....81.....340.....1238......3891......10761.......26764........60988
...8...53....340....1920.....9075.....36292.....125892......387849......1082111
..15..142...1238....9075....54376....271846....1165921.....4396009.....14863460
..26..339...3891...36292...271846...1679072....8807722....40232545....163307844
..42..729..10761..125892..1165921...8807722...55960651...306796310...1481748658
..64.1437..26764..387849..4396009..40232545..306796310..2001017650..11403395172
..93.2638..60988.1082111.14863460.163307844.1481748658.11403395172..76084625352
.130.4568.129236.2777103.45791493.598768118.6411737114.57777817522.448101581256
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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: [polynomial of degree 6]
k=3: [polynomial of degree 9]
k=4: [polynomial of degree 12]
k=5: [polynomial of degree 15]
k=6: [polynomial of degree 18]
k=7: [polynomial of degree 21]
Empirical for "within 1" instead of "within 3" is T(n,k)=binomial(n+k,k)-1
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..0..1....0..1..2..3....0..0..1..2....0..0..1..1....0..1..2..2
..0..1..1..2....1..2..2..3....1..1..2..2....0..1..1..1....1..1..2..2
..0..1..2..3....2..3..3..4....1..2..2..3....0..1..2..2....1..1..2..2
..1..2..3..4....3..3..3..4....2..2..2..3....1..2..2..3....1..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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