%I #4 Mar 25 2018 11:38:18

%S 0,1,1,1,3,1,2,10,10,2,3,23,30,23,3,5,61,118,118,61,5,8,162,407,564,

%T 407,162,8,13,421,1498,2793,2793,1498,421,13,21,1103,5289,14394,21224,

%U 14394,5289,1103,21,34,2890,19184,71564,146841,146841,71564,19184,2890,34,55

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 4 horizontally or vertically adjacent elements, with upper left element zero.

%C Table starts

%C ..0....1.....1.......2........3..........5...........8............13

%C ..1....3....10......23.......61........162.........421..........1103

%C ..1...10....30.....118......407.......1498........5289.........19184

%C ..2...23...118.....564.....2793......14394.......71564........359659

%C ..3...61...407....2793....21224.....146841.....1073621.......7703565

%C ..5..162..1498...14394...146841....1537496....15498505.....159497778

%C ..8..421..5289...71564..1073621...15498505...225780260....3307561389

%C .13.1103.19184..359659..7703565..159497778..3307561389...68862687289

%C .21.2890.68832.1808256.55506215.1631501428.48158543096.1434208027966

%H R. H. Hardin, <a href="/A301669/b301669.txt">Table of n, a(n) for n = 1..197</a>

%F Empirical for column k:

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

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

%F k=3: [order 20]

%F k=4: [order 70]

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000045(n-1).

%Y Column 2 is A185828.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Mar 25 2018