A302010 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 240, 128, 16, 32, 512, 1808, 1808, 512, 32, 64, 2048, 13616, 25808, 13616, 2048, 64, 128, 8192, 102544, 369040, 368144, 102544, 8192, 128, 256, 32768, 772272, 5276816, 9989376, 5251712, 772272, 32768, 256, 512, 131072

Offset: 1

Author

R. H. Hardin, Mar 30 2018

Keywords

• nonn
• tabl

Comments

Table starts

...1......2........4...........8............16...............32

...2......8.......32.........128...........512.............2048

...4.....32......240........1808.........13616...........102544

...8....128.....1808.......25808........369040..........5276816

..16....512....13616......368144.......9989376........270990144

..32...2048...102544.....5251712.....270422672......13918667808

..64...8192...772272....74917424....7320574992.....714887543376

.128..32768..5816080..1068722240..198174358400...36717919842624

.256.131072.43801648.15245681888.5364752820144.1885898831169344

Examples

			Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..0
..1..0..0..1. .1..0..1..0. .0..1..0..1. .1..1..0..0. .0..0..1..0
..0..1..0..0. .0..0..1..1. .1..1..1..0. .0..0..1..0. .0..0..0..1
..1..1..1..1. .1..1..0..0. .0..0..0..0. .0..1..0..0. .1..1..0..1
..0..1..0..1. .0..0..1..0. .0..1..0..0. .1..1..1..0. .0..0..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..479

Crossrefs

Column 1 and row 1 are A000079(n-1).

Column 2 and row 2 are A004171(n-1).

Column 3 and row 3 are A301779.

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

k=2: a(n) = 4*a(n-1)

k=3: a(n) = 7*a(n-1) +4*a(n-2)

k=4: a(n) = 13*a(n-1) +18*a(n-2) +a(n-3) -4*a(n-4)

k=5: a(n) = 24*a(n-1) +82*a(n-2) +34*a(n-3) -90*a(n-4) -40*a(n-5) +37*a(n-6)

k=6: [order 10] for n>12

k=7: [order 17] for n>19

Empirical for row n:

n=1: a(n) = 2*a(n-1)

n=2: a(n) = 4*a(n-1)

n=3: a(n) = 7*a(n-1) +4*a(n-2)

n=4: a(n) = 13*a(n-1) +20*a(n-2) -16*a(n-3) -64*a(n-4) for n>6

n=5: [order 12] for n>15

n=6: [order 32] for n>36

n=7: [order 78] for n>83