A299746 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 6 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 31, 31, 8, 16, 121, 179, 121, 16, 32, 472, 1073, 1073, 472, 32, 64, 1841, 6479, 10150, 6479, 1841, 64, 128, 7181, 39015, 97462, 97462, 39015, 7181, 128, 256, 28010, 235033, 932318, 1502630, 932318, 235033, 28010, 256, 512, 109255, 1416220

Offset

1,2

Comments

Table starts

...1......2.......4.........8..........16............32..............64

...2......8......31.......121.........472..........1841............7181

...4.....31.....179......1073........6479.........39015..........235033

...8....121....1073.....10150.......97462........932318.........8918662

..16....472....6479.....97462.....1502630......23034971.......353167830

..32...1841...39015....932318....23034971.....564998177.....13855907809

..64...7181..235033...8918662...353167830...13855907809....543386033722

.128..28010.1416220..85379274..5421997554..340475803209..21367169090398

.256.109255.8533123.817325435.83244577728.8367066746663.840301228632106

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: [order 10] for n>11

k=4: [order 37] for n>38

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A281831.

Column 3 is A298996.

Column 4 is A298997.

Sequence in context: A299081 A299844 A299001 * A299668 A300259 A305523

Adjacent sequences: A299743 A299744 A299745 * A299747 A299748 A299749

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 18 2018

Status

approved