A298287 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 6 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 25, 25, 8, 16, 85, 70, 85, 16, 32, 286, 205, 205, 286, 32, 64, 969, 614, 649, 614, 969, 64, 128, 3281, 1860, 2151, 2151, 1860, 3281, 128, 256, 11114, 5631, 7006, 8264, 7006, 5631, 11114, 256, 512, 37649, 17034, 22768, 29673, 29673, 22768

Offset

1,2

Comments

Table starts

...1.....2.....4......8......16......32.......64.......128........256

...2.....8....25.....85.....286.....969.....3281.....11114......37649

...4....25....70....205.....614....1860.....5631.....17034......51507

...8....85...205....649....2151....7006....22768.....73751.....238775

..16...286...614...2151....8264...29673...104357....369220....1307146

..32...969..1860...7006...29673..121368...484412...1948367....7872325

..64..3281..5631..22768..104357..484412..2195114..10198130...48049615

.128.11114.17034..73751..369220.1948367.10198130..55665676..310280107

.256.37649.51507.238775.1307146.7872325.48049615.310280107.2065512284

Links

R. H. Hardin, Table of n, a(n) for n = 1..337

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5)

k=3: [order 11] for n>12

k=4: [order 24] for n>27

Example

Some solutions for n=6 k=4
..0..0..0..0. .0..1..1..0. .0..0..1..1. .0..1..0..1. .0..1..1..1
..1..1..1..1. .1..0..0..1. .0..1..0..0. .0..1..0..1. .0..0..1..0
..0..0..0..0. .1..1..1..1. .0..1..0..1. .0..1..0..1. .1..1..1..1
..0..1..1..0. .0..0..0..0. .1..1..0..1. .1..0..1..0. .0..0..0..0
..1..0..0..1. .1..1..1..1. .0..1..0..1. .1..0..1..0. .1..0..1..1
..1..1..1..1. .1..0..0..1. .0..1..0..1. .1..0..0..1. .0..0..0..1

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A281338.

Sequence in context: A240484 A240636 A281344 * A299359 A299180 A299942

Adjacent sequences: A298284 A298285 A298286 * A298288 A298289 A298290

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 16 2018

Status

approved