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A266067
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T(n,k)=Number of nXk integer arrays with each element equal to the number of horizontal, vertical, diagonal and antidiagonal neighbors exactly one smaller than itself.
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6
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1, 3, 3, 4, 17, 4, 5, 35, 35, 5, 9, 89, 34, 89, 9, 16, 323, 81, 81, 323, 16, 25, 1057, 809, 525, 809, 1057, 25, 39, 3027, 1750, 8262, 8262, 1750, 3027, 39, 64, 9257, 5071, 25663, 154939, 25663, 5071, 9257, 64, 105, 29835, 29256, 148323, 1066148, 1066148, 148323
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OFFSET
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1,2
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COMMENTS
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Table starts
...1.....3......4.......5.........9........16........25.........39.........64
...3....17.....35......89.......323......1057......3027.......9257......29835
...4....35.....34......81.......809......1750......5071......29256......93170
...5....89.....81.....525......8262.....25663....148323....1480037....7361668
...9...323....809....8262....154939...1066148..11753249..164649556.1624261580
..16..1057...1750...25663...1066148..11211992.156829155.3678276863
..25..3027...5071..148323..11753249.156829155
..39..9257..29256.1480037.164649556
..64.29835..93170.7361668
.105.92561.300067
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1) +a(n-3) +a(n-4)
k=2: [order 18]
k=3: [order 78]
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..0..1....2..1..0..0....1..0..0..1....1..0..0..0....1..1..2..0
..0..2..3..2....1..3..2..0....2..2..2..2....1..2..3..0....0..2..2..1
..1..1..2..1....2..0..3..1....1..3..3..1....2..2..2..0....0..3..2..2
..2..3..2..0....1..2..1..2....0..1..1..0....0..1..2..1....0..0..0..1
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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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