A301669 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 4 horizontally or vertically adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 10, 10, 2, 3, 23, 30, 23, 3, 5, 61, 118, 118, 61, 5, 8, 162, 407, 564, 407, 162, 8, 13, 421, 1498, 2793, 2793, 1498, 421, 13, 21, 1103, 5289, 14394, 21224, 14394, 5289, 1103, 21, 34, 2890, 19184, 71564, 146841, 146841, 71564, 19184, 2890, 34, 55

Offset

1,5

Comments

Table starts

..0....1.....1.......2........3..........5...........8............13

..1....3....10......23.......61........162.........421..........1103

..1...10....30.....118......407.......1498........5289.........19184

..2...23...118.....564.....2793......14394.......71564........359659

..3...61...407....2793....21224.....146841.....1073621.......7703565

..5..162..1498...14394...146841....1537496....15498505.....159497778

..8..421..5289...71564..1073621...15498505...225780260....3307561389

.13.1103.19184..359659..7703565..159497778..3307561389...68862687289

.21.2890.68832.1808256.55506215.1631501428.48158543096.1434208027966

Links

R. H. Hardin, Table of n, a(n) for n = 1..197

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = 2*a(n-1) +a(n-2) +2*a(n-3) -a(n-4)

k=3: [order 20]

k=4: [order 70]

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A185828.

Sequence in context: A316757 A055450 A185835 * A300427 A300689 A300612

Adjacent sequences: A301666 A301667 A301668 * A301670 A301671 A301672

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 25 2018

Status

approved