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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.

%I A240656 #6 Jul 23 2025 11:05:41
%S A240656 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 A240656 136,352,352,136,21,1,1,42,402,1545,2456,1545,402,42,1,1,86,1180,7154,
%U A240656 16629,16629,7154,1180,86,1,1,179,3518,33269,118863,184819,118863,33269,3518
%N 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.
%C A240656 Table starts
%C A240656 .1...1.....1......1........1..........1............1..............1
%C A240656 .1...2.....2......3........6.........10...........21.............42
%C A240656 .1...2.....9.....17.......43........136..........402...........1180
%C A240656 .1...3....17.....91......352.......1545.........7154..........33269
%C A240656 .1...6....43....352.....2456......16629.......118863.........863435
%C A240656 .1..10...136...1545....16629.....184819......2076117.......23697768
%C A240656 .1..21...402...7154...118863....2076117.....37066859......666849212
%C A240656 .1..42..1180..33269...863435...23697768....666849212....18940533171
%C A240656 .1..86..3518.154974..6296517..272201307..12062165754...540011330454
%C A240656 .1.179.10525.724237.46082534.3137010024.218944306666.15442088872458
%H A240656 R. H. Hardin, <a href="/A240656/b240656.txt">Table of n, a(n) for n = 1..220</a>
%F A240656 Empirical for column k:
%F A240656 k=1: a(n) = a(n-1)
%F A240656 k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
%F A240656 k=3: [order 15]
%F A240656 k=4: [order 50]
%e A240656 Some solutions for n=4 k=4
%e A240656 ..0..0..0..0....0..0..0..0....0..1..1..0....0..1..1..1....0..1..1..1
%e A240656 ..0..1..0..0....0..0..1..0....1..1..1..1....1..1..1..1....1..1..1..1
%e A240656 ..0..0..1..1....0..0..0..0....1..1..0..1....1..1..1..1....1..1..1..0
%e A240656 ..0..0..1..1....0..0..0..0....0..1..1..1....0..1..1..0....1..1..0..1
%Y A240656 Column 2 is A240513(n-2)
%K A240656 nonn,tabl
%O A240656 1,5
%A A240656 _R. H. Hardin_, Apr 09 2014