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

1,4

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A001629.

Column 2 is A093967.

Sequence in context: A202395 A117903 A167685 * A120493 A085880 A055883

Adjacent sequences: A268737 A268738 A268739 * A268741 A268742 A268743

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 12 2016

Status

approved