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A241370
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T(n,k)=Number of nXk 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order
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14
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1, 1, 2, 2, 7, 5, 4, 28, 47, 14, 8, 121, 460, 326, 41, 16, 523, 4617, 7376, 2284, 122, 32, 2261, 46245, 169982, 118488, 16026, 365, 64, 9775, 463567, 3910194, 6280325, 1904096, 112458, 1094, 128, 42261, 4646421, 90008909, 332185927, 232173463
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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..............4.................8...................16
....2.......7.........28............121...............523.................2261
....5......47........460...........4617.............46245...............463567
...14.....326.......7376.........169982...........3910194.............90008909
...41....2284.....118488........6280325.........332185927..........17583615124
..122...16026....1904096......232173463.......28238828935........3437694358689
..365..112458...30598800.....8582759752.....2400505507498......672068364873884
.1094..789166..491723328...317280724429...204061855414167...131390467341043995
.3281.5537942.7902006144.11729003927933.17346886991310331.25687100469219790719
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 4*a(n-1) -3*a(n-2)
k=2: a(n) = 7*a(n-1) +2*a(n-3) -8*a(n-4) for n>5
k=3: [order 8]
k=4: [order 31]
k=5: [order 94]
Empirical for row n:
n=1: a(n) = 2*a(n-1) for n>2
n=2: a(n) = 5*a(n-1) -2*a(n-2) -4*a(n-3) for n>5
n=3: a(n) = 9*a(n-1) +16*a(n-2) -50*a(n-3) -72*a(n-4) -32*a(n-5) -32*a(n-6) for n>8
n=4: [order 21] for n>23
n=5: [order 65] for n>67
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..0..1....0..1..0..2....0..1..0..2....0..1..0..2....0..1..0..2
..1..1..2..0....1..0..2..1....0..2..0..0....2..0..0..1....0..1..2..1
..1..2..2..0....2..0..0..1....1..2..0..0....1..0..2..0....2..0..1..0
..1..2..2..1....0..1..0..2....0..1..0..1....2..0..1..2....1..0..1..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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