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A240893
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T(n,k)=Number of nXk 0..2 arrays with no element equal to a different number of vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order
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7
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1, 1, 1, 2, 4, 2, 4, 11, 11, 4, 8, 36, 57, 36, 8, 16, 116, 289, 289, 116, 16, 32, 376, 1485, 2362, 1485, 376, 32, 64, 1216, 7609, 19065, 19065, 7609, 1216, 64, 128, 3936, 38981, 154858, 245268, 154858, 38981, 3936, 128, 256, 12736, 199761, 1255585, 3146755
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OFFSET
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1,4
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COMMENTS
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Table starts
...1.....1.......2.........4...........8.............16...............32
...1.....4......11........36.........116............376.............1216
...2....11......57.......289........1485...........7609............38981
...4....36.....289......2362.......19065.........154858..........1255585
...8...116....1485.....19065......245268........3146755.........40424861
..16...376....7609....154858.....3146755.......64074526.......1302610899
..32..1216...38981...1255585....40424861.....1302610899......41971040844
..64..3936..199761..10186158...519218802....26501432610....1352138182759
.128.12736.1023597..82615013..6669141957...539075345618...43565815810587
.256.41216.5245049.670126562.85661208693.10966382557858.1403705064843757
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1) for n>2
k=2: a(n) = 2*a(n-1) +4*a(n-2) for n>4
k=3: a(n) = 3*a(n-1) +8*a(n-2) +14*a(n-3) +4*a(n-4)
k=4: [order 16]
k=5: [order 48]
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..2..1....0..1..2..0....0..1..1..0....0..1..2..1....0..1..2..0
..1..2..1..0....2..0..0..1....2..1..1..2....2..0..1..2....1..2..0..2
..2..1..0..2....1..0..0..2....1..0..0..1....1..2..0..1....0..0..2..1
..1..2..1..0....2..1..2..0....2..0..0..2....0..1..2..0....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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