%I #6 Apr 05 2020 21:09:20

%S 0,0,0,0,0,0,0,5,5,0,0,30,50,30,0,1,126,538,538,126,1,3,520,3932,8270,

%T 3932,520,3,10,2088,32253,123706,123706,32253,2088,10,24,8192,238532,

%U 1853532,3584756,1853532,238532,8192,24,60,32083,1875212,27938670

%N T(n,k) = Number of n X k 0..1 arrays with the number of 1's horizontally or vertically adjacent to some 0 two less than the number of 0's adjacent to some 1.

%C Table starts

%C ..0.....0........0..........0.............0................1..................3

%C ..0.....0........5.........30...........126..............520...............2088

%C ..0.....5.......50........538..........3932............32253.............238532

%C ..0....30......538.......8270........123706..........1853532...........27938670

%C ..0...126.....3932.....123706.......3584756........108110791.........3229944132

%C ..1...520....32253....1853532.....108110791.......6394436704.......382399996325

%C ..3..2088...238532...27938670....3229944132.....382399996325.....45587718323826

%C .10..8192..1875212..424161696...98063836816...23061514189084...5491408595796062

%C .24.32083.14222474.6473516290.2979455186170.1399727072882973.665386690317576640

%H R. H. Hardin, <a href="/A286979/b286979.txt">Table of n, a(n) for n = 1..143</a>

%e Some solutions for n=4, k=4

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

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

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

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

%Y Column 1 is A286209.

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_, May 17 2017