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%I #4 Apr 06 2014 14:14:17
%S 1,2,2,4,8,4,8,25,25,8,16,81,122,81,16,32,264,578,578,264,32,64,857,
%T 2753,4104,2753,857,64,128,2785,13147,29084,29084,13147,2785,128,256,
%U 9050,62781,205754,306749,205754,62781,9050,256,512,29407,299758,1455916
%N T(n,k)=Number of nXk 0..1 arrays with no element equal to more than two horizontal or vertical neighbors, with new values 0..1 introduced in row major order
%C Table starts
%C ...1.....2.......4.........8..........16............32..............64
%C ...2.....8......25........81.........264...........857............2785
%C ...4....25.....122.......578........2753.........13147...........62781
%C ...8....81.....578......4104.......29084........205754.........1455916
%C ..16...264....2753.....29084......306749.......3229199........33986995
%C ..32...857...13147....205754.....3229199......50525365.......790390105
%C ..64..2785...62781...1455916....33986995.....790390105.....18384693920
%C .128..9050..299758..10304849...357678069...12362251350....427494590110
%C .256.29407.1431221..72937769..3764378216..193349390970...9939634161916
%C .512.95557.6833530.516249590.39618451066.3024029579084.231101074704277
%H R. H. Hardin, <a href="/A240484/b240484.txt">Table of n, a(n) for n = 1..263</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
%F k=3: a(n) = 4*a(n-1) +3*a(n-2) +2*a(n-3) +6*a(n-4) +2*a(n-5) -a(n-6)
%F k=4: [order 22]
%F k=5: [order 54]
%e Some solutions for n=4 k=4
%e ..0..0..0..1....0..1..1..0....0..0..1..1....0..1..0..1....0..0..0..1
%e ..1..1..1..0....0..0..1..0....1..0..1..0....0..1..0..0....0..1..1..0
%e ..0..0..1..0....1..0..1..0....0..1..0..0....1..0..1..0....0..1..0..1
%e ..0..1..0..1....1..0..1..0....0..0..1..1....1..0..0..0....0..1..0..1
%Y Column 1 is A000079(n-1)
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Apr 06 2014
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