%I #11 Jun 19 2020 04:01:43

%S 126,441,441,1785,2401,1785,7225,14161,14161,7225,27880,83521,127449,

%T 83521,27880,107584,485809,1147041,1147041,485809,107584,422136,

%U 2825761,9967797,15752961,9967797,2825761,422136,1656369,16475481,86620249

%N T(n,k)=Number of (n+2)X(k+2) binary arrays avoiding patterns 000 and 010 in rows and columns.

%H R. H. Hardin, <a href="/A202406/b202406.txt">Table of n, a(n) for n = 1..418</a>

%e Table starts

%e ......126........441.........1785...........7225.............27880

%e ......441.......2401........14161..........83521............485809

%e .....1785......14161.......127449........1147041...........9967797

%e .....7225......83521......1147041.......15752961.........204518601

%e ....27880.....485809......9967797......204518601........4005967518

%e ...107584....2825761.....86620249.....2655237841.......78466093924

%e ...422136...16475481....761992011....35242177441.....1562067102398

%e ..1656369...96059601...6703188129...467758877041....31096917284521

%e ..6459453..559842921..58683373353..6151258109929...615218671150193

%e .25190361.3262808641.513746331121.80892053988001.12171431974069369

%e ...

%e Some solutions for n=2 k=3

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 19 2011