A295652 - OEIS

%I #4 Nov 25 2017 08:39:25

%S 2,4,4,7,11,7,13,35,35,13,24,106,184,106,24,44,327,956,956,327,44,81,

%T 1003,4993,8391,4993,1003,81,149,3082,26037,74335,74335,26037,3082,

%U 149,274,9465,135848,657178,1117226,657178,135848,9465,274,504,29073,708695

%N T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 1, 3 or 4 1s.

%C Table starts

%C ...2.....4.......7........13..........24............44..............81

%C ...4....11......35.......106.........327..........1003............3082

%C ...7....35.....184.......956........4993.........26037..........135848

%C ..13...106.....956......8391.......74335........657178.........5812860

%C ..24...327....4993.....74335.....1117226......16755140.......251412699

%C ..44..1003...26037....657178....16755140.....426233396.....10849299317

%C ..81..3082..135848...5812860...251412699...10849299317....468469936974

%C .149..9465..708695..51408810..3772052117..276124405949..20225972157848

%C .274.29073.3697224.454678898.56595784982.7027872154812.873281057421907

%H R. H. Hardin, <a href="/A295652/b295652.txt">Table of n, a(n) for n = 1..241</a>

%F Empirical for column k:

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

%F k=2: a(n) = 2*a(n-1) +3*a(n-2) +a(n-3) -a(n-5)

%F k=3: [order 18]

%F k=4: [order 45]

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A000073(n+3).

%Y Column 2 is A295247.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 25 2017