A268766 T(n,k)=Number of nXk binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

0, 1, 1, 2, 6, 2, 5, 15, 15, 5, 10, 44, 56, 44, 10, 20, 105, 223, 223, 105, 20, 38, 258, 762, 1148, 762, 258, 38, 71, 595, 2607, 5170, 5170, 2607, 595, 71, 130, 1368, 8500, 23156, 32056, 23156, 8500, 1368, 130, 235, 3069, 27411, 99057, 193573, 193573, 99057

Offset: 1

Author

R. H. Hardin, Feb 13 2016

Keywords

• nonn
• tabl

Comments

Table starts

...0....1......2.......5........10.........20...........38............71

...1....6.....15......44.......105........258..........595..........1368

...2...15.....56.....223.......762.......2607.........8500.........27411

...5...44....223....1148......5170......23156........99057........418924

..10..105....762....5170.....32056.....193573......1129042.......6475898

..20..258...2607...23156....193573....1552272.....12111209......92571436

..38..595...8500...99057...1129042...12111209....127676872....1312123185

..71.1368..27411..418924...6475898...92571436...1312123185...18045771274

.130.3069..86622.1736105..36505596..696659613..13311824510..245588158242

.235.6830.270955.7122856.203462597.5178525870.133228716170.3292985469950

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1404

Crossrefs

Column 1 is A001629.

Column 2 is A193449.

Formula

Empirical for column k:

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

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

k=3: a(n) = 4*a(n-1) +2*a(n-2) -16*a(n-3) -a(n-4) +12*a(n-5) -4*a(n-6)

k=4: [order 8]

k=5: [order 12]

k=6: [order 16]

k=7: [order 28]