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%I #5 Mar 31 2012 12:36:44
%S 0,2,2,2,4,2,3,8,8,3,4,14,18,14,4,5,23,47,47,23,5,6,36,118,191,118,36,
%T 6,7,54,273,752,752,273,54,7,8,78,585,2732,4860,2732,585,78,8,9,109,
%U 1174,9111,29540,29540,9111,1174,109,9,10,148,2228,28011,164704,310036,164704
%N T(n,k)=Number of nXk 0..1 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor
%C Table starts
%C .0...2....2......3........4..........5............6..............7
%C .2...4....8.....14.......23.........36...........54.............78
%C .2...8...18.....47......118........273..........585...........1174
%C .3..14...47....191......752.......2732.........9111..........28011
%C .4..23..118....752.....4860......29540.......164704.........838248
%C .5..36..273...2732....29540.....310036......3030673.......27104947
%C .6..54..585...9111...164704....3030673.....53350918......867792264
%C .7..78.1174..28011...838248...27104947....867792264....26097731070
%C .8.109.2228..79918..3906802..220732437..12855063828...718921134406
%C .9.148.4030.213153.16781171.1641106829.173064550218.17996760930623
%H R. H. Hardin, <a href="/A201353/b201353.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical: T(n,k) is a polynomial in n of degree 2^k-1 for n>2,1,1,4,10,22,46 for k in 1..7
%e Some solutions for n=10 k=3
%e ..0..0..1....0..0..0....0..0..0....0..1..1....0..0..0....0..0..0....0..0..0
%e ..0..0..1....0..0..0....0..0..1....0..1..1....0..1..1....0..0..0....0..0..0
%e ..0..1..1....0..0..0....0..0..1....0..1..1....0..1..1....0..0..0....0..0..0
%e ..0..1..1....0..1..1....0..0..1....0..1..1....0..1..1....0..0..1....0..0..0
%e ..0..1..1....1..0..0....0..1..1....0..1..1....1..0..0....0..1..1....0..0..1
%e ..1..0..0....1..0..1....0..1..1....0..1..1....1..0..1....1..0..0....0..1..1
%e ..1..1..0....1..0..1....0..1..1....1..0..0....1..0..1....1..0..0....1..0..1
%e ..1..1..0....1..1..1....1..0..0....1..1..1....1..0..1....1..1..0....1..0..1
%e ..1..1..1....1..1..1....1..0..1....1..1..1....1..0..1....1..1..0....1..0..1
%e ..1..1..1....1..1..1....1..1..1....1..1..1....1..1..1....1..1..0....1..1..1
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Nov 30 2011
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