%I #4 Feb 19 2016 08:44:48

%S 2,4,4,7,11,8,13,27,32,16,23,76,123,89,32,41,185,521,537,244,64,72,

%T 489,1887,3288,2343,659,128,126,1204,7477,17713,20400,10167,1760,256,

%U 219,3059,27042,102545,165607,123976,43959,4657,512,379,7539,102070,542112

%N T(n,k)=Number of nXk binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

%C Table starts

%C ....2.....4.......7........13..........23...........41.............72

%C ....4....11......27........76.........185..........489...........1204

%C ....8....32.....123.......521........1887.........7477..........27042

%C ...16....89.....537......3288.......17713.......102545.........542112

%C ...32...244....2343.....20400......165607......1383105.......10778640

%C ...64...659...10167....123976.....1529241.....18220241......210476400

%C ..128..1760...43959....742688....14011359....236272677.....4064720816

%C ..256..4657..189465...4397376...127528641...3024972401....77785162880

%C ..512.12228..814359..25791040..1154377943..38333973609..1477636398784

%C .1024.31899.3491691.150081504.10400164377.481701017577.27897108860960

%H R. H. Hardin, <a href="/A269075/b269075.txt">Table of n, a(n) for n = 1..721</a>

%F Empirical for column k:

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

%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) = 10*a(n-1) -31*a(n-2) +24*a(n-3) +21*a(n-4) -18*a(n-5) -9*a(n-6)

%F k=4: a(n) = 12*a(n-1) -40*a(n-2) +8*a(n-3) +92*a(n-4) -32*a(n-5) -64*a(n-6) for n>7

%F k=5: [order 12]

%F k=6: [order 14]

%F k=7: [order 24] for n>25

%F Empirical for row n:

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

%F n=2: a(n) = 2*a(n-1) +5*a(n-2) -6*a(n-3) -9*a(n-4)

%F n=3: a(n) = 4*a(n-1) +8*a(n-2) -34*a(n-3) -16*a(n-4) +60*a(n-5) -25*a(n-6)

%F n=4: [order 8]

%F n=5: [order 14]

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A000079.

%Y Column 2 is A268744.

%Y Row 1 is A208354(n+1).

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 19 2016