A298294 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4 or 6 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 7, 4, 8, 13, 13, 8, 16, 29, 20, 29, 16, 32, 69, 26, 26, 69, 32, 64, 137, 43, 46, 43, 137, 64, 128, 301, 72, 130, 130, 72, 301, 128, 256, 705, 115, 233, 308, 233, 115, 705, 256, 512, 1461, 189, 448, 515, 515, 448, 189, 1461, 512, 1024, 3193, 318, 877, 1084

Offset

1,2

Comments

Table starts

...1....2...4....8...16...32....64...128....256....512....1024....2048....4096

...2....7..13...29...69..137...301...705...1461...3193....7373...15729...34405

...4...13..20...26...43...72...115...189....318....526.....874....1473....2482

...8...29..26...46..130..233...448...877...1605...3284....6774...13516...26780

..16...69..43..130..308..515..1084..2374...4754..10042...21207...44405...93926

..32..137..72..233..515..990..1798..4079...9026..18246...39612...86150..184768

..64..301.115..448.1084.1798..4679.10688..22503..53875..123435..278930..642076

.128..705.189..877.2374.4079.10688.26963..60768.151924..370070..871422.2153007

.256.1461.318.1605.4754.9026.22503.60768.153319.389464.1009970.2538759.6516314

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) -2*a(n-2) +8*a(n-3) -20*a(n-4) +8*a(n-5) for n>6

k=3: [order 17] for n>19

k=4: [order 67] for n>70

Example

Some solutions for n=7 k=4
..0..1..0..1. .0..0..0..1. .0..1..1..0. .0..0..1..0. .0..0..1..0
..0..0..0..1. .1..1..1..0. .0..0..1..0. .1..1..1..0. .1..0..1..0
..0..0..1..0. .0..1..1..0. .1..1..1..0. .0..1..0..1. .0..0..1..0
..1..0..0..1. .1..0..1..0. .0..1..0..1. .0..1..0..1. .1..1..1..1
..0..0..0..0. .1..0..1..1. .0..1..0..1. .0..1..0..1. .0..1..0..0
..1..1..1..1. .1..0..1..1. .1..1..1..0. .1..0..0..0. .0..1..0..1
..0..0..0..0. .1..0..1..0. .0..0..1..0. .1..0..1..1. .0..1..0..0

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A297883.

Sequence in context: A203975 A270246 A297889 * A299388 A298494 A299187

Adjacent sequences: A298291 A298292 A298293 * A298295 A298296 A298297

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 16 2018

Status

approved