%I #4 Jun 14 2015 16:27:07
%S 512,2736,2736,11872,15416,11872,51856,86968,86968,51856,222400,
%T 510095,659792,510095,222400,914112,2769733,5271330,5271330,2769733,
%U 914112,3644672,14722533,38603552,58411404,38603552,14722533,3644672,14254784
%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock diagonal median plus antidiagonal median nondecreasing horizontally and vertically
%C Table starts
%C ......512......2736.......11872........51856.........222400..........914112
%C .....2736.....15416.......86968.......510095........2769733........14722533
%C ....11872.....86968......659792......5271330.......38603552.......279149887
%C ....51856....510095.....5271330.....58411404......575237942......5661517795
%C ...222400...2769733....38603552....575237942.....7595409032....100897843080
%C ...914112..14722533...279149887...5661517795...100897843080...1832394625108
%C ..3644672..77704089..2026873370..55658584373..1346660412346..33594417416223
%C .14254784.402403692.14414890711.532429444542.17454653713101.594433786098630
%H R. H. Hardin, <a href="/A258910/b258910.txt">Table of n, a(n) for n = 1..144</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 22]
%e Some solutions for n=2 k=4
%e ..0..0..0..0..0..1....0..0..0..1..1..1....0..0..0..1..0..1....0..0..0..1..1..0
%e ..1..0..0..0..0..1....1..1..0..0..0..1....1..0..0..0..0..0....1..0..1..1..1..1
%e ..1..0..0..0..1..1....0..0..0..0..0..0....1..0..0..1..1..1....0..1..1..1..1..1
%e ..0..0..0..0..1..0....1..0..0..0..0..1....1..0..0..1..1..1....0..1..0..1..0..0
%Y Column 1 is A253986
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jun 14 2015