A300380 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 10, 4, 10, 1, 1, 13, 11, 11, 13, 1, 1, 42, 8, 26, 8, 42, 1, 1, 74, 58, 80, 80, 58, 74, 1, 1, 188, 131, 237, 389, 237, 131, 188, 1, 1, 387, 306, 692, 1351, 1351, 692, 306, 387, 1, 1, 885, 936, 2548, 6577, 8839, 6577, 2548, 936, 885, 1, 1, 1937

Offset

1,5

Comments

Table starts

.1...1...1....1......1.......1........1.........1..........1............1

.1...3...2...10.....13......42.......74.......188........387..........885

.1...2...4...11......8......58......131.......306........936.........2435

.1..10..11...26.....80.....237......692......2548.......8240........26808

.1..13...8...80....389....1351.....6577.....29663.....128834.......599170

.1..42..58..237...1351....8839....53367....330577....2105279.....13511213

.1..74.131..692...6577...53367...481311...4070089...36505624....319929622

.1.188.306.2548..29663..330577..4070089..47968011..590197943...7181318177

.1.387.936.8240.128834.2105279.36505624.590197943.9905247305.168928472097

Links

R. H. Hardin, Table of n, a(n) for n = 1..238

Formula

Empirical for column k:

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

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

k=3: [order 23] for n>25

k=4: [order 80] for n>82

Example

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

Crossrefs

Sequence in context: A073166 A050169 A143214 * A300682 A300605 A301330

Adjacent sequences: A300377 A300378 A300379 * A300381 A300382 A300383

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 04 2018

Status

approved