A300682 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 10, 5, 10, 1, 1, 13, 11, 11, 13, 1, 1, 42, 8, 28, 8, 42, 1, 1, 74, 58, 80, 80, 58, 74, 1, 1, 188, 131, 245, 398, 245, 131, 188, 1, 1, 387, 306, 729, 1382, 1382, 729, 306, 387, 1, 1, 885, 936, 2604, 6686, 9015, 6686, 2604, 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...5...11......8......58......131.......306.........936.........2435

.1..10..11...28.....80.....245......729......2604........8579........27943

.1..13...8...80....398....1382.....6686.....30218......131674.......611429

.1..42..58..245...1382....9015....54361....338173.....2152660.....13818749

.1..74.131..729...6686...54361...494771...4174087....37464671....329141039

.1.188.306.2604..30218..338173..4174087..49274326...607495472...7403455976

.1.387.936.8579.131674.2152660.37464671.607495472.10215309343.174419385580

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

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>26

k=4: [order 82] for n>84

Example

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

Crossrefs

Column 2 is A300374.

Sequence in context: A050169 A143214 A300380 * A300605 A301330 A175636

Adjacent sequences: A300679 A300680 A300681 * A300683 A300684 A300685

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 11 2018

Status

approved