A297720 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1, 2 or 4 neighboring 1s.

1, 2, 1, 4, 10, 1, 7, 34, 29, 1, 12, 83, 145, 87, 1, 21, 258, 523, 747, 280, 1, 37, 865, 2717, 4212, 4090, 876, 1, 65, 2651, 14462, 36981, 34319, 21116, 2735, 1, 114, 8041, 68919, 336653, 512354, 268630, 110551, 8583, 1, 200, 25114, 332306, 2699832, 8103241

Offset: 1

Author

R. H. Hardin, Jan 04 2018

Keywords

• nonn
• tabl

Comments

Table starts

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

.1....10......34........83.........258...........865............2651

.1....29.....145.......523........2717.........14462...........68919

.1....87.....747......4212.......36981........336653.........2699832

.1...280....4090.....34319......512354.......8103241.......107787351

.1...876...21116....268630.....6812856.....183324631......4021047904

.1..2735..110551...2139403....91994155....4238895126....154327332017

.1..8583..582755..17031173..1242370107...98184350818...5920531350715

.1.26900.3055652.135252357.16741579726.2265008802005.226188909640209

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..180

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 13]

k=4: [order 42]

k=5: [order 87]

Empirical for row n:

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

n=2: a(n) = 4*a(n-1) -3*a(n-2) +3*a(n-3) -2*a(n-4) -24*a(n-5) +24*a(n-6)

n=3: [order 18]

n=4: [order 51]