A188824 T(n,k) = number of n X k binary arrays without the pattern 0 1 diagonally or antidiagonally.

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

Offset: 1

Author

R. H. Hardin, Apr 11 2011

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1627

Crossrefs

Column 2 is A000290(n+1).

Column 4 is A016802.

Row 2 is A007598(n+2).

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