A268740 T(n,k)=Number of nXk binary arrays with some 1 horizontally or vertically adjacent to some other 1 exactly once.

0, 1, 1, 2, 4, 2, 5, 15, 15, 5, 10, 48, 80, 48, 10, 20, 145, 396, 396, 145, 20, 38, 420, 1788, 2876, 1788, 420, 38, 71, 1183, 7831, 19591, 19591, 7831, 1183, 71, 130, 3264, 33170, 128232, 200204, 128232, 33170, 3264, 130, 235, 8865, 137868, 816009, 1971414

Offset: 1

Author

R. H. Hardin, Feb 12 2016

Keywords

• nonn
• tabl

Comments

Table starts

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

...1.....4......15........48.........145...........420...........1183

...2....15......80.......396........1788..........7831..........33170

...5....48.....396......2876.......19591........128232.........816009

..10...145....1788.....19591......200204.......1971414.......18847982

..20...420....7831....128232.....1971414......29134076......418632185

..38..1183...33170....816009....18847982.....418632185.....9039552112

..71..3264..137868...5087814...176668038....5894815754...191307160577

.130..8865..563486..31228804..1629738420...81718671716..3985770068310

.235.23780.2275119.189328186.14851460143.1119014223138.82030747371058

Examples

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

Links

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

Crossrefs

Column 1 is A001629.

Column 2 is A093967.

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) = 4*a(n-1) -2*a(n-2) -4*a(n-3) -a(n-4)

k=3: a(n) = 4*a(n-1) +8*a(n-2) -24*a(n-3) -38*a(n-4) +4*a(n-5) +12*a(n-6) -a(n-8)

k=4: [order 10]

k=5: [order 18]

k=6: [order 22]

k=7: [order 42]