A268740 - OEIS

%I #4 Feb 12 2016 08:47:01

%S 0,1,1,2,4,2,5,15,15,5,10,48,80,48,10,20,145,396,396,145,20,38,420,

%T 1788,2876,1788,420,38,71,1183,7831,19591,19591,7831,1183,71,130,3264,

%U 33170,128232,200204,128232,33170,3264,130,235,8865,137868,816009,1971414

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

%C Table starts

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

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

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

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

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

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

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

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

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

%C .235.23780.2275119.189328186.14851460143.1119014223138.82030747371058

%H R. H. Hardin, <a href="/A268740/b268740.txt">Table of n, a(n) for n = 1..1404</a>

%F Empirical for column k:

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

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

%F 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)

%F k=4: [order 10]

%F k=5: [order 18]

%F k=6: [order 22]

%F k=7: [order 42]

%e Some solutions for n=4 k=4

%e ..0..1..0..1. .0..0..0..1. .0..1..0..1. .0..0..1..0. .0..1..0..0

%e ..1..0..0..0. .1..0..0..0. .0..0..0..1. .1..1..0..0. .1..0..0..1

%e ..0..1..0..1. .0..1..1..0. .0..0..0..0. .0..0..1..0. .0..1..1..0

%e ..0..0..0..1. .1..0..0..0. .1..0..1..0. .0..0..0..0. .1..0..0..0

%Y Column 1 is A001629.

%Y Column 2 is A093967.

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Feb 12 2016