A297506 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

1, 2, 1, 4, 10, 1, 7, 31, 29, 1, 12, 68, 110, 87, 1, 21, 218, 314, 531, 280, 1, 37, 729, 1829, 2281, 2534, 876, 1, 65, 2097, 8803, 23348, 14201, 11405, 2735, 1, 114, 6139, 34757, 191192, 270845, 88808, 53175, 8583, 1, 200, 18932, 157673, 1247716, 3624914

Offset: 1

Author

R. H. Hardin, Dec 31 2017

Keywords

• nonn
• tabl

Comments

Table starts

.1.....2.......4........7.........12...........21.............37

.1....10......31.......68........218..........729...........2097

.1....29.....110......314.......1829.........8803..........34757

.1....87.....531.....2281......23348.......191192........1247716

.1...280....2534....14201.....270845......3624914.......35049871

.1...876...11405....88808....3075264.....66289769......978288822

.1..2735...53175...573119...35919085...1272836591....28914051279

.1..8583..246040..3613793..414559944..23896899569...823340493402

.1.26900.1135117.22999331.4794512057.450529429259.23748019543354

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..242

Crossrefs

Column 2 is A295525.

Row 1 is A005251(n+2).

Formula

Empirical for column k:

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

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

k=3: [order 11]

k=4: [order 18]

k=5: [order 50]

Empirical for row n:

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

n=2: a(n) = 3*a(n-1) -2*a(n-2) +9*a(n-3) -6*a(n-4) -8*a(n-5)

n=3: [order 10]

n=4: [order 24]

n=5: [order 59]