A317118 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 30, 30, 8, 16, 112, 142, 112, 16, 32, 420, 698, 698, 420, 32, 64, 1576, 3398, 5157, 3398, 1576, 64, 128, 5912, 16686, 37221, 37221, 16686, 5912, 128, 256, 22176, 81809, 273221, 392393, 273221, 81809, 22176, 256, 512, 83184, 401415

Offset

1,2

Comments

Table starts

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

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

...4....30.....142.......698.......3398........16686..........81809

...8...112.....698......5157......37221.......273221........2000595

..16...420....3398.....37221.....392393......4237829.......45938893

..32..1576...16686....273221....4237829.....67247490.....1080066752

..64..5912...81809...2000595...45938893...1080066752....25956605294

.128.22176..401415..14657917..497129492..17278502991...620005212254

.256.83184.1969107.107409094.5387633738.277268412729.14887658798448

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 10] for n>12

k=4: [order 35] for n>37

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A281949.

Sequence in context: A281955 A316183 A305769 * A305530 A317004 A316822

Adjacent sequences: A317115 A317116 A317117 * A317119 A317120 A317121

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 21 2018

Status

approved