%I
%S 512,729,729,1000,1194,1000,1331,1876,1876,1331,1728,2835,3362,2835,
%T 1728,2197,4137,5735,5735,4137,2197,2744,5854,9338,10918,9338,5854,
%U 2744,3375,8064,14586,19614,19614,14586,8064,3375,4096,10851,21972,33468,38478
%N T(n,k)=Number of (n+2)X(k+2) binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column
%C Table starts
%C ..512...729..1000...1331...1728....2197....2744....3375.....4096.....4913
%C ..729..1194..1876...2835...4137....5854....8064...10851....14305....18522
%C .1000..1876..3362...5735...9338...14586...21972...32073....45556....63184
%C .1331..2835..5735..10918..19614...33468...54618...85779...130333...192425
%C .1728..4137..9338..19614..38478...71088..124740..209445...338596...529731
%C .2197..5854.14586..33468..71088..141192..264822..473031...810265..1338508
%C .2744..8064.21972..54618.124740..264822..528390.1000023..1808746..3145568
%C .3375.10851.32073..85779.209445..473031.1000023.1998486..3805510..6949194
%C .4096.14305.45556.130333.338596..810265.1808746.3805510..7609118.14556230
%C .4913.18522.63184.192425.529731.1338508.3145568.6949194.14556230.29110180
%H R. H. Hardin, <a href="/A202461/b202461.txt">Table of n, a(n) for n = 1..9378</a>
%e Some solutions for 8X8
%e ..0..0..0..0..0..0....0..0..0..0..0..1....0..0..0..0..0..0....0..0..0..0..0..0
%e ..0..0..0..0..0..0....0..0..1..1..1..1....0..0..0..0..0..0....0..0..0..0..0..0
%e ..0..0..0..0..0..0....0..0..1..1..1..1....0..0..0..0..0..0....0..0..0..0..0..1
%e ..0..0..0..1..0..0....0..0..1..1..1..1....0..0..0..0..0..0....0..0..0..0..0..1
%e ..0..0..0..1..0..0....0..0..1..1..1..1....0..0..0..0..0..0....0..0..0..0..0..1
%e ..0..0..0..1..1..1....0..0..1..1..1..1....0..0..0..0..1..1....0..0..0..1..0..1
%e ..0..0..0..1..1..0....0..1..1..1..1..1....0..1..1..1..1..1....0..0..0..0..0..1
%e ..0..1..1..1..1..1....0..0..1..1..1..1....0..1..1..1..1..1....0..0..0..0..1..1
%Y Column 1 is A000578(n+7)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Dec 19 2011
