%I #4 Dec 17 2017 13:17:29
%S 2,3,3,5,8,5,8,19,19,8,13,47,71,47,13,21,116,260,260,116,21,34,286,
%T 966,1444,966,286,34,55,705,3581,8042,8042,3581,705,55,89,1738,13275,
%U 44783,67488,44783,13275,1738,89,144,4285,49209,249329,565149,565149,249329
%N T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0, 2 or 4 neighboring 1s.
%C Table starts
%C ..2....3......5.......8........13..........21...........34.............55
%C ..3....8.....19......47.......116.........286..........705...........1738
%C ..5...19.....71.....260.......966........3581........13275..........49209
%C ..8...47....260....1444......8042.......44783.......249329........1388229
%C .13..116....966....8042.....67488......565149......4733229.......39643699
%C .21..286...3581...44783....565149.....7121315.....89713772.....1130293195
%C .34..705..13275..249329...4733229....89713772...1700240351....32223940011
%C .55.1738..49209.1388229..39643699..1130293195..32223940011...918770773688
%C .89.4285.182422.7729475.332039800.14240708558.610746699603.26197140564540
%H R. H. Hardin, <a href="/A296635/b296635.txt">Table of n, a(n) for n = 1..311</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = a(n-1) +2*a(n-2) +3*a(n-3) +2*a(n-4) +a(n-5)
%F k=3: [order 12]
%F k=4: [order 39]
%e Some solutions for n=5 k=4
%e ..0..1..1..0. .0..1..0..1. .0..0..0..1. .0..0..0..0. .1..1..0..1
%e ..1..0..1..0. .0..0..0..0. .0..1..0..0. .1..0..1..0. .1..0..0..0
%e ..1..1..0..0. .1..0..0..1. .0..0..0..0. .0..0..0..1. .0..0..1..1
%e ..0..0..1..0. .0..1..0..0. .0..0..0..0. .0..1..0..0. .1..0..1..0
%e ..0..0..0..1. .0..0..0..0. .0..0..0..0. .0..0..1..0. .0..1..1..0
%Y Column 1 is A000045(n+2).
%Y Column 2 is A296329.
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 17 2017