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A188824 T(n,k) = number of n X k binary arrays without the pattern 0 1 diagonally or antidiagonally. 13
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
LINKS
FORMULA
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
EXAMPLE
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
CROSSREFS
Column 2 is A000290(n+1).
Column 4 is A016802.
Row 2 is A007598(n+2).
Sequence in context: A107848 A285273 A353946 * A181212 A233394 A029599
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 11 2011
STATUS
approved

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Last modified April 17 21:22 EDT 2024. Contains 371767 sequences. (Running on oeis4.)