A300498 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 7, 4, 8, 18, 18, 8, 16, 50, 52, 50, 16, 32, 138, 143, 143, 138, 32, 64, 383, 412, 499, 412, 383, 64, 128, 1063, 1225, 1513, 1513, 1225, 1063, 128, 256, 2951, 3699, 4686, 5837, 4686, 3699, 2951, 256, 512, 8193, 11243, 14822, 19412, 19412, 14822, 11243

Offset

1,2

Comments

Table starts

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

...2....7....18.....50....138.....383.....1063......2951......8193......22748

...4...18....52....143....412....1225.....3699.....11243.....34012.....102446

...8...50...143....499...1513....4686....14822.....46717....149232.....478952

..16..138...412...1513...5837...19412....66166....233796....816547....2856851

..32..383..1225...4686..19412...77582...291721...1136238...4513729...17926620

..64.1063..3699..14822..66166..291721..1296506...5589526..24694845..110652439

.128.2951.11243..46717.233796.1136238..5589526..28067098.138863892..695711878

.256.8193.34012.149232.816547.4513729.24694845.138863892.789286221.4445350963

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) = 3*a(n-1) -a(n-2) +a(n-3) +a(n-4) -2*a(n-5) -a(n-6)

k=3: [order 24] for n>25

k=4: [order 83] for n>86

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A280598.

Sequence in context: A300314 A280604 A301323 * A300937 A300881 A301491

Adjacent sequences: A300495 A300496 A300497 * A300499 A300500 A300501

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 07 2018

Status

approved