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A268740 T(n,k)=Number of nXk binary arrays with some 1 horizontally or vertically adjacent to some other 1 exactly once. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified February 23 17:23 EST 2018. Contains 299584 sequences. (Running on oeis4.)