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A240656 T(n,k)=Number of nXk 0..1 arrays with no element equal to exactly one horizontal or vertical neighbor, with new values 0..1 introduced in row major order 7

%I

%S 1,1,1,1,2,1,1,2,2,1,1,3,9,3,1,1,6,17,17,6,1,1,10,43,91,43,10,1,1,21,

%T 136,352,352,136,21,1,1,42,402,1545,2456,1545,402,42,1,1,86,1180,7154,

%U 16629,16629,7154,1180,86,1,1,179,3518,33269,118863,184819,118863,33269,3518

%N T(n,k)=Number of nXk 0..1 arrays with no element equal to exactly one horizontal or vertical neighbor, with new values 0..1 introduced in row major order

%C Table starts

%C .1...1.....1......1........1..........1............1..............1

%C .1...2.....2......3........6.........10...........21.............42

%C .1...2.....9.....17.......43........136..........402...........1180

%C .1...3....17.....91......352.......1545.........7154..........33269

%C .1...6....43....352.....2456......16629.......118863.........863435

%C .1..10...136...1545....16629.....184819......2076117.......23697768

%C .1..21...402...7154...118863....2076117.....37066859......666849212

%C .1..42..1180..33269...863435...23697768....666849212....18940533171

%C .1..86..3518.154974..6296517..272201307..12062165754...540011330454

%C .1.179.10525.724237.46082534.3137010024.218944306666.15442088872458

%H R. H. Hardin, <a href="/A240656/b240656.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1)

%F k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)

%F k=3: [order 15]

%F k=4: [order 50]

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 2 is A240513(n-2)

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Apr 09 2014

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Last modified February 22 19:52 EST 2019. Contains 320403 sequences. (Running on oeis4.)