A305530 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4 or 6 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 30, 30, 8, 16, 112, 161, 112, 16, 32, 420, 880, 880, 420, 32, 64, 1576, 4779, 7385, 4779, 1576, 64, 128, 5912, 26000, 61139, 61139, 26000, 5912, 128, 256, 22176, 141474, 506359, 767417, 506359, 141474, 22176, 256, 512, 83184, 769617

Offset

1,2

Comments

Table starts

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

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

...4....30.....161.......880........4779.........26000.........141474

...8...112.....880......7385.......61139........506359........4205030

..16...420....4779.....61139......767417.......9599897......120736482

..32..1576...26000....506359.....9599897.....180860170.....3433486971

..64..5912..141474...4205030...120736482....3433486971....98651246976

.128.22176..769617..34889423..1516911265...65111777047..2831187189412

.256.83184.4187055.289444806.19047231319.1233566348589.81130991759635

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]

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

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A281949.

Sequence in context: A316183 A305769 A317118 * A317004 A316822 A317572

Adjacent sequences: A305527 A305528 A305529 * A305531 A305532 A305533

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 04 2018

Status

approved