A299359 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 6 or 8 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, 8269, 7006, 5631, 11114, 256, 512, 37649, 17034, 22768, 29682, 29682, 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....8269...29682...104376....369294....1307456

..32...969..1860...7006...29682..121386...484468...1948622....7873597

..64..3281..5631..22768..104376..484468..2195326..10199011...48054411

.128.11114.17034..73751..369294.1948622.10199011..55671460..310306752

.256.37649.51507.238775.1307456.7873597.48054411.310306752.2065637548

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=5 k=4
..0..1..0..0. .0..1..0..1. .0..1..0..0. .0..1..1..0. .0..1..0..0
..0..1..1..1. .0..1..0..1. .0..1..1..0. .1..0..1..0. .1..0..1..0
..0..0..0..0. .0..1..0..1. .0..0..1..0. .0..0..1..0. .1..0..1..1
..1..1..1..0. .0..1..0..1. .1..0..1..0. .1..0..1..0. .1..0..1..0
..0..0..0..1. .1..1..0..1. .1..0..1..1. .1..0..1..1. .1..0..0..1

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A281338.

Column 3 is A298282.

Column 4 is A298283.

Sequence in context: A240636 A281344 A298287 * A299180 A299942 A301841

Adjacent sequences: A299356 A299357 A299358 * A299360 A299361 A299362

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 08 2018

Status

approved