A304848 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 12, 12, 8, 16, 24, 25, 24, 16, 32, 64, 51, 51, 64, 32, 64, 184, 165, 132, 165, 184, 64, 128, 432, 419, 502, 502, 419, 432, 128, 256, 1088, 1009, 1638, 3009, 1638, 1009, 1088, 256, 512, 2944, 2697, 4816, 12763, 12763, 4816, 2697, 2944, 512, 1024

Offset

1,2

Comments

Table starts

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

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

...4...12...25....51....165.....419.....1009......2697........7091........18147

...8...24...51...132....502....1638.....4816.....15697.......51711.......162366

..16...64..165...502...3009...12763....45988....205950......912997......3690448

..32..184..419..1638..12763...67025...294924...1719748.....9770201.....48882277

..64..432.1009..4816..45988..294924..1500288..10862979....74522808....445537503

.128.1088.2697.15697.205950.1719748.10862979.105482136...961899269...7444841268

.256.2944.7091.51711.912997.9770201.74522808.961899269.11448808957.111429411031

Links

R. H. Hardin, Table of n, a(n) for n = 1..263

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..1..0. .0..0..1..0. .0..0..1..1. .0..0..0..0. .0..1..0..0
..0..1..0..0. .0..0..1..0. .0..0..0..0. .0..1..0..0. .1..0..0..0
..0..0..0..0. .0..0..0..0. .0..0..1..1. .1..0..0..0. .0..0..0..0
..1..0..0..0. .0..0..0..0. .1..1..1..1. .1..1..0..0. .0..0..0..1
..0..1..0..0. .0..0..1..1. .1..1..1..1. .1..0..1..0. .0..0..1..0

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A303794.

Sequence in context: A305245 A304479 A316304 * A316545 A306060 A317238

Adjacent sequences: A304845 A304846 A304847 * A304849 A304850 A304851

Keyword

nonn,tabl

Author

R. H. Hardin, May 19 2018

Status

approved