A300208 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 248, 128, 16, 32, 512, 1933, 1933, 512, 32, 64, 2048, 15070, 29561, 15070, 2048, 64, 128, 8192, 117494, 451996, 451996, 117494, 8192, 128, 256, 32768, 916061, 6912249, 13548425, 6912249, 916061, 32768, 256, 512, 131072

Offset

1,2

Comments

Table starts

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

...2......8.......32.........128............512.............2048

...4.....32......248........1933..........15070...........117494

...8....128.....1933.......29561.........451996..........6912249

..16....512....15070......451996.......13548425........406228452

..32...2048...117494.....6912249......406228452......23883950854

..64...8192...916061...105708560....12180207076....1404241937017

.128..32768..7142233..1616600364...365209429387...82562348427139

.256.131072.55685704.24722667407.10950385677546.4854250928660105

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

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

k=3: a(n) = 8*a(n-1) -2*a(n-2) +5*a(n-3) -13*a(n-4) -6*a(n-5)

k=4: [order 15]

k=5: [order 38]

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Sequence in context: A316808 A299654 A317525 * A303421 A301407 A213418

Adjacent sequences: A300205 A300206 A300207 * A300209 A300210 A300211

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 28 2018

Status

approved