A303800 T(n,k) = Number of n X k 0..1 arrays with every element unequal to 0, 1, 2 or 4 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 12, 12, 8, 16, 24, 17, 24, 16, 32, 64, 30, 30, 64, 32, 64, 184, 70, 90, 70, 184, 64, 128, 432, 121, 231, 231, 121, 432, 128, 256, 1088, 221, 631, 562, 631, 221, 1088, 256, 512, 2944, 421, 1586, 1406, 1406, 1586, 421, 2944, 512, 1024, 7360, 800

Offset

1,2

Comments

Table starts

...1....2...4.....8....16.....32....64....128....256.....512....1024.....2048

...2....4..12....24....64....184...432...1088...2944....7360...18496....48384

...4...12..17....30....70....121...221....421....800....1511....2832.....5340

...8...24..30....90...231....631..1586...4230..11059...29053...75910...199512

..16...64..70...231...562...1406..2829...7014..16337...38826...88805...212475

..32..184.121...631..1406...5282.11733..41444.108170..344248..929630..2892458

..64..432.221..1586..2829..11733.15478..67090..96021..421513..602782..2643954

.128.1088.421..4230..7014..41444.67090.394667.764127.3928166.8156073.39226935

.256.2944.800.11059.16337.108170.96021.764127.587035.6174082.3728099.50846990

Links

R. H. Hardin, Table of n, a(n) for n = 1..543

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: a(n) = a(n-1) +a(n-2) +2*a(n-3) -a(n-5) -2*a(n-6) -2*a(n-7) for n>10

k=4: [order 28] for n>32

k=5: [order 18] for n>24

k=6: [order 71] for n>75

k=7: [order 63] for n>71

Example

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

Crossrefs

Column 1 is A000079(n-1).

Sequence in context: A133389 A320196 A033740 * A305245 A304479 A316304

Adjacent sequences: A303797 A303798 A303799 * A303801 A303802 A303803

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 30 2018

Status

approved