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A207024
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T(n,k) = Number of n X k 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
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12
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2, 4, 4, 6, 16, 6, 9, 36, 36, 8, 13, 81, 90, 64, 10, 18, 169, 252, 168, 100, 12, 25, 324, 624, 558, 270, 144, 14, 34, 625, 1350, 1586, 1035, 396, 196, 16, 46, 1156, 3025, 3726, 3315, 1719, 546, 256, 18, 62, 2116, 6256, 9450, 8280, 6123, 2646, 720, 324, 20, 83, 3844
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OFFSET
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1,1
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COMMENTS
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Table starts
..2...4...6....9....13....18.....25.....34......46......62.......83......111
..4..16..36...81...169...324....625...1156....2116....3844.....6889....12321
..6..36..90..252...624..1350...3025...6256...12788...25792....50630....99012
..8..64.168..558..1586..3726...9450..21318...47518..104470...220531...464202
.10.100.270.1035..3315..8280..23400..56814..136114..322834...725005..1627260
.12.144.396.1719..6123.16038..49925.129302..329498..836938..1984447..4716834
.14.196.546.2646.10374.28224..95900.263228..707756.1914436..4765030.11929281
.16.256.720.3852.16484.46260.170300.492932.1389476.3984244.10362550.27202659
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*n
k=2: a(n) = 4*n^2
k=3: a(n) = 12*n^2 - 6*n
k=4: a(n) = 6*n^3 + (27/2)*n^2 - (21/2)*n
k=5: a(n) = (13/6)*n^4 + 13*n^3 + (52/3)*n^2 - (39/2)*n
k=6: a(n) = (33/4)*n^4 + (45/2)*n^3 + (75/4)*n^2 - (63/2)*n
k=7: a(n) = (55/24)*n^5 + (75/4)*n^4 + (275/8)*n^3 + (75/4)*n^2 - (295/6)*n
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EXAMPLE
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Some solutions for n=4, k=3
..1..0..0....0..1..0....0..0..1....1..0..1....0..0..1....1..1..0....1..1..1
..1..0..0....1..1..0....1..1..1....0..0..1....0..0..1....1..0..1....1..1..1
..1..0..0....1..1..0....0..0..1....0..0..1....0..0..1....1..0..1....0..1..0
..1..0..0....1..0..0....0..0..1....0..0..1....0..0..1....0..0..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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