A301906 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.

1, 1, 2, 1, 1, 4, 1, 2, 1, 8, 1, 2, 3, 1, 16, 1, 3, 2, 7, 1, 32, 1, 6, 2, 5, 16, 1, 64, 1, 10, 7, 8, 10, 43, 1, 128, 1, 21, 12, 40, 12, 26, 117, 1, 256, 1, 42, 27, 96, 92, 64, 65, 330, 1, 512, 1, 86, 62, 316, 320, 532, 196, 170, 935, 1, 1024, 1, 179, 160, 1078, 1588, 1934, 1999, 864, 442

Offset: 1

Author

R. H. Hardin, Mar 28 2018

Keywords

• nonn
• tabl

Comments

Table starts

...1.1...1...1....1.....1......1.......1........1..........1...........1

...2.1...2...2....3.....6.....10......21.......42.........86.........179

...4.1...3...2....2.....7.....12......27.......62........160.........387

...8.1...7...5....8....40.....96.....316.....1078.......3831.......13331

..16.1..16..10...12....92....320....1588.....7234......34477......171770

..32.1..43..26...64...532...1934...14860....86638.....568382.....4029337

..64.1.117..65..196..1999...8781..104732...770376....7398173....75183520

.128.1.330.170..864.10150..49709..952467..8263384..113474387..1620307756

.256.1.935.442.3236.46226.253844.7931939.81388360.1622304450.32687652025

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..287

Crossrefs

Column 1 is A000079(n-1).

Column 4 is A245306(n-1).

Row 2 is A240513(n-3).

Formula

Empirical for column k:

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

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

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

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

k=5: a(n) = 4*a(n-1) +5*a(n-2) -20*a(n-3) -4*a(n-4) +16*a(n-5) for n>6

k=6: [order 20] for n>21

k=7: [order 30] for n>33

Empirical for row n:

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

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

n=3: [order 30] for n>31