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A241328
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T(n,k)=Number of nXk 0..3 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order
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11
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1, 1, 2, 2, 8, 5, 5, 59, 85, 15, 14, 530, 2344, 1030, 51, 41, 4877, 68935, 95144, 13011, 187, 122, 45057, 2034543, 8949808, 3875244, 165924, 715, 365, 416533, 60066019, 842185933, 1162535788, 157912026, 2121033, 2795, 1094, 3851085, 1773370241
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OFFSET
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1,3
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COMMENTS
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Table starts
...1.......1..........2..............5................14....................41
...2.......8.........59............530..............4877.................45057
...5......85.......2344..........68935...........2034543..............60066019
..15....1030......95144........8949808.........842185933...........79254376889
..51...13011....3875244.....1162535788......348722168314.......104609549355169
.187..165924..157912026...151022716125...144410575985227....138095118530911728
.715.2121033.6435036610.19619065042282.59802363257355728.182299462522915741748
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 7*a(n-1) -14*a(n-2) +8*a(n-3)
k=2: [order 9] for n>10
k=3: [order 15]
k=4: [order 53]
Empirical for row n:
n=1: a(n) = 4*a(n-1) -3*a(n-2) for n>3
n=2: a(n) = 12*a(n-1) -26*a(n-2) +2*a(n-3) +28*a(n-4) -6*a(n-5) -9*a(n-6) for n>8
n=3: [order 11] for n>13
n=4: [order 36] for n>38
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EXAMPLE
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Some solutions for n=3 k=4
..0..1..0..1....0..1..2..1....0..1..2..1....0..1..0..2....0..1..0..1
..1..0..1..2....1..0..2..3....0..2..3..0....1..2..0..1....2..0..3..2
..1..0..3..0....0..2..0..1....1..3..2..3....3..2..1..3....3..1..2..0
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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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