A317004 T(n,k)=Number of nXk 0..1 arrays with every element unequal 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, 30, 30, 8, 16, 112, 162, 112, 16, 32, 420, 894, 894, 420, 32, 64, 1576, 4905, 7665, 4905, 1576, 64, 128, 5912, 26952, 65047, 65047, 26952, 5912, 128, 256, 22176, 148138, 551591, 854383, 551591, 148138, 22176, 256, 512, 83184, 814090

Offset

1,2

Comments

Table starts

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

...2.....8......30.......112.........420..........1576............5912

...4....30.....162.......894........4905.........26952..........148138

...8...112.....894......7665.......65047........551591.........4691054

..16...420....4905.....65047......854383......11158663.......146589898

..32..1576...26952....551591....11158663.....223714229......4522081307

..64..5912..148138...4691054...146589898....4522081307....140997597309

.128.22176..814090..39872525..1924812465...91395911298...4396796733747

.256.83184.4474116.338839996.25259268302.1845641069555.136949793274310

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

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

k=4: [order 38] for n>39

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A281949.

Sequence in context: A305769 A317118 A305530 * A316822 A317572 A281837

Adjacent sequences: A317001 A317002 A317003 * A317005 A317006 A317007

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 18 2018

Status

approved