A259642 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000000 or 00000001

18, 29, 29, 69, 64, 69, 133, 171, 171, 133, 236, 365, 581, 365, 236, 472, 813, 1483, 1483, 813, 472, 940, 1964, 3849, 4146, 3849, 1964, 940, 1781, 4499, 11261, 12348, 12348, 11261, 4499, 1781, 3433, 10188, 30957, 42524, 44500, 42524, 30957, 10188, 3433

Offset

1,1

Comments

Table starts

...18....29.....69.....133......236.......472........940........1781

...29....64....171.....365......813......1964.......4499.......10188

...69...171....581....1483.....3849.....11261......30957.......82977

..133...365...1483....4146....12348.....42524.....133078......406770

..236...813...3849...12348....44500....182654.....670088.....2436036

..472..1964..11261...42524...182654....899557....3919925....16946757

..940..4499..30957..133078...670088...3919925...19848497...100074919

.1781.10188..82977..406770..2436036..16946757..100074919...593505391

.3433.23712.231015.1313046..9361060..77735408..540718241..3793818370

.6725.54825.639787.4180198.35240824.348525973.2836175763.23386045739

Links

R. H. Hardin, Table of n, a(n) for n = 1..684

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +a(n-2) +5*a(n-3) +a(n-4) -3*a(n-5) -3*a(n-6) for n>7

k=3: [order 9] for n>10

k=4: [order 12] for n>13

k=5: [order 24] for n>25

k=6: [order 30] for n>32

k=7: [order 42] for n>44

Example

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

Crossrefs

Sequence in context: A180117 A339633 A167333 * A045000 A205871 A144833

Adjacent sequences: A259639 A259640 A259641 * A259643 A259644 A259645

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 02 2015

Status

approved