A297314 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 or 2 neighboring 1s.

1, 2, 1, 4, 7, 1, 7, 23, 21, 1, 12, 66, 117, 65, 1, 21, 207, 497, 609, 200, 1, 37, 654, 2577, 3808, 3159, 616, 1, 65, 2049, 13937, 35476, 29212, 16389, 1897, 1, 114, 6422, 72541, 340825, 484808, 223995, 85041, 5842, 1, 200, 20119, 375054, 2997197, 8273245

Offset: 1

Author

R. H. Hardin, Dec 28 2017

Keywords

• nonn
• tabl

Comments

Table starts

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

.1.....7......23........66.........207...........654............2049

.1....21.....117.......497........2577.........13937...........72541

.1....65.....609......3808.......35476........340825.........2997197

.1...200....3159.....29212......484808.......8273245.......121339476

.1...616...16389....223995.....6623719.....200646607......4893232934

.1..1897...85041...1717882....90535227....4869858862....197589351469

.1..5842..441225..13174266..1237278512..118156684121...7976248015498

.1.17991.2289339.101033369.16909630099.2867120332406.322003901582689

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..447

Crossrefs

Column 2 is A218836.

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) +3*a(n-2) +a(n-3)

k=3: a(n) = 3*a(n-1) +11*a(n-2) +3*a(n-3) -6*a(n-4)

k=4: [order 8] for n>9

k=5: [order 12] for n>14

k=6: [order 22] for n>25

k=7: [order 35] for n>39

Empirical for row n:

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

n=2: [order 9]

n=3: [order 23]

n=4: [order 61]