A316545 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 12, 12, 8, 16, 24, 26, 24, 16, 32, 64, 53, 53, 64, 32, 64, 184, 187, 136, 187, 184, 64, 128, 432, 484, 568, 568, 484, 432, 128, 256, 1088, 1262, 1874, 4219, 1874, 1262, 1088, 256, 512, 2944, 3570, 5966, 19819, 19819, 5966, 3570, 2944, 512, 1024

Offset

1,2

Comments

Table starts

...1....2....4.....8......16.......32........64........128..........256

...2....4...12....24......64......184.......432.......1088.........2944

...4...12...26....53.....187......484......1262.......3570.........9751

...8...24...53...136.....568.....1874......5966......20721........70789

..16...64..187...568....4219....19819.....85583.....452386......2248258

..32..184..484..1874...19819...114514....674392....4849500.....31884846

..64..432.1262..5966...85583...674392...5074646...49303976....433518999

.128.1088.3570.20721..452386..4849500..49303976..681913008...8395255440

.256.2944.9751.70789.2248258.31884846.433518999.8395255440.140688693646

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

Formula

Empirical for column k:

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

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

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

k=4: [order 34] for n>38

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A303794.

Sequence in context: A304479 A316304 A304848 * A306060 A317238 A260038

Adjacent sequences: A316542 A316543 A316544 * A316546 A316547 A316548

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 06 2018

Status

approved