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A188824
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T(n,k) = number of n X k binary arrays without the pattern 0 1 diagonally or antidiagonally.
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13
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2, 4, 4, 8, 9, 8, 16, 25, 16, 16, 32, 64, 48, 25, 32, 64, 169, 144, 81, 36, 64, 128, 441, 432, 256, 120, 49, 128, 256, 1156, 1296, 841, 400, 169, 64, 256, 512, 3025, 3888, 2704, 1360, 576, 224, 81, 512, 1024, 7921, 11664, 8836, 4624, 2025, 784, 289, 100, 1024, 2048
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OFFSET
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1,1
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COMMENTS
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Table starts
....2...4...8...16...32....64...128....256.....512....1024.....2048.....4096
....4...9..25...64..169...441..1156...3025....7921...20736....54289...142129
....8..16..48..144..432..1296..3888..11664...34992..104976...314928...944784
...16..25..81..256..841..2704..8836..28561...93025..301401...980100..3179089
...32..36.120..400.1360..4624.15776..53824..183744..627264..2141568..7311616
...64..49.169..576.2025..7056.24964..87616..310249.1092025..3865156.13623481
..128..64.224..784.2800.10000.36000.129600..468000.1690000..6110000.22090000
..256..81.289.1024.3721.13456.49284.179776..660969.2421136..8916196.32729841
..512.100.360.1296.4752.17424.64416.238144..884256.3283344.12220128.45481536
.1024.121.441.1600.5929.21904.81796.304704.1142761.4276624.16080100.60341824
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LINKS
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FORMULA
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Empirical: a(n,1) = 2^n
Empirical: a(n,2) = n^2 + 2*n + 1
Empirical: a(n,3) = 2*a(n-1,3) - 2*a(n-3,3) + a(n-4,3)
Empirical: a(n,4) = 16*n^2
Empirical: a(n,5) = 2*a(n-1,5) - 2*a(n-3,5) + a(n-4,5) for n>5
Empirical: a(n,6) = 256*n^2 - 384*n + 144 for n>2
Empirical: a(n,7) = 2*a(n-1,7) - 2*a(n-3,7) + a(n-4,7) for n>7
Empirical: a(n,8) = 4096*n^2 - 11264*n + 7744 for n>4
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EXAMPLE
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Some solutions for 5X3
..1..1..1....1..1..1....1..1..1....1..1..1....1..1..1....0..1..0....1..1..1
..1..1..1....0..1..1....1..0..1....1..1..1....1..1..1....1..0..1....1..1..1
..1..1..1....0..0..1....0..1..0....1..1..1....0..1..0....0..1..0....0..1..1
..1..1..1....0..0..0....0..0..0....0..0..0....0..0..0....1..0..1....1..0..1
..1..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....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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