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A252829
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T(n,k)=Number of nXk nonnegative integer arrays with upper left 0 and every value within 1 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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1
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1, 2, 2, 3, 5, 3, 4, 9, 9, 4, 5, 13, 21, 13, 5, 6, 17, 37, 37, 17, 6, 7, 21, 53, 85, 53, 21, 7, 8, 25, 69, 149, 149, 69, 25, 8, 9, 29, 85, 213, 341, 213, 85, 29, 9, 10, 33, 101, 277, 597, 597, 277, 101, 33, 10, 11, 37, 117, 341, 853, 1365, 853, 341, 117, 37, 11, 12, 41, 133, 405
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OFFSET
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1,2
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COMMENTS
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Table starts
..1..2...3...4....5....6.....7.....8......9.....10.....11.....12......13
..2..5...9..13...17...21....25....29.....33.....37.....41.....45......49
..3..9..21..37...53...69....85...101....117....133....149....165.....181
..4.13..37..85..149..213...277...341....405....469....533....597.....661
..5.17..53.149..341..597...853..1109...1365...1621...1877...2133....2389
..6.21..69.213..597.1365..2389..3413...4437...5461...6485...7509....8533
..7.25..85.277..853.2389..5461..9557..13653..17749..21845..25941...30037
..8.29.101.341.1109.3413..9557.21845..38229..54613..70997..87381..103765
..9.33.117.405.1365.4437.13653.38229..87381.152917.218453.283989..349525
.10.37.133.469.1621.5461.17749.54613.152917.349525.611669.873813.1135957
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 1*n
k=2: a(n) = 4*n - 3 for n>1
k=3: a(n) = 16*n - 27 for n>2
k=4: a(n) = 64*n - 171 for n>3
k=5: a(n) = 256*n - 939 for n>4
k=6: a(n) = 1024*n - 4779 for n>5
k=7: a(n) = 4096*n - 23211 for n>6
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..1..2....0..1..2..2....0..1..2..2....0..1..1..2....0..1..2..2
..0..1..1..2....1..1..2..2....1..1..2..2....1..1..2..2....1..1..2..2
..1..1..2..2....2..2..2..2....1..1..2..3....2..2..2..2....2..2..2..2
..2..2..2..2....2..2..2..3....2..2..2..3....2..2..3..3....2..3..3..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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