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A240649 T(n,k)=Number of nXk 0..1 arrays with no element equal to the same number of vertical neighbors as horizontal neighbors, with new values 0..1 introduced in row major order.

%I A240649 #6 Jul 23 2025 11:05:01
%S A240649 0,1,1,1,2,1,2,2,2,2,3,3,6,3,3,5,6,8,8,6,5,8,10,23,18,23,10,8,13,21,
%T A240649 60,61,61,60,21,13,21,42,149,168,232,168,149,42,21,34,86,396,526,953,
%U A240649 953,526,396,86,34,55,179,1050,1643,4343,5304,4343,1643,1050,179,55,89,370
%N A240649 T(n,k)=Number of nXk 0..1 arrays with no element equal to the same number of vertical neighbors as horizontal neighbors, with new values 0..1 introduced in row major order.
%C A240649 Table starts
%C A240649 ..0...1....1.....2......3.......5.........8.........13..........21...........34
%C A240649 ..1...2....2.....3......6......10........21.........42..........86..........179
%C A240649 ..1...2....6.....8.....23......60.......149........396........1050.........2814
%C A240649 ..2...3....8....18.....61.....168.......526.......1643........5524........18762
%C A240649 ..3...6...23....61....232.....953......4343......19458.......90165.......421048
%C A240649 ..5..10...60...168....953....5304.....29481.....168320......990468......5920658
%C A240649 ..8..21..149...526...4343...29481....227270....1748201....14230080....116070258
%C A240649 .13..42..396..1643..19458..168320...1748201...18030130...191002776...2052931147
%C A240649 .21..86.1050..5524..90165..990468..14230080..191002776..2764522654..39961388170
%C A240649 .34.179.2814.18762.421048.5920658.116070258.2052931147.39961388170.770199142784
%H A240649 R. H. Hardin, <a href="/A240649/b240649.txt">Table of n, a(n) for n = 1..220</a>
%F A240649 Empirical for column k:
%F A240649 k=1: a(n) = a(n-1) +a(n-2)
%F A240649 k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
%F A240649 k=3: [order 20]
%F A240649 k=4: [order 48]
%e A240649 Some solutions for n=4 k=4
%e A240649 ..0..0..0..1....0..0..0..0....0..1..0..0....0..0..1..1....0..0..0..0
%e A240649 ..1..1..1..1....1..0..1..1....0..1..1..1....1..1..0..0....1..1..0..1
%e A240649 ..0..1..0..1....1..0..0..0....0..1..0..0....0..0..1..1....0..0..0..1
%e A240649 ..0..1..0..1....1..0..1..1....1..1..1..1....1..1..0..0....1..1..0..1
%Y A240649 Column 1 is A000045(n-1)
%Y A240649 Column 2 is A240513(n-2)
%K A240649 nonn,tabl
%O A240649 1,5
%A A240649 _R. H. Hardin_, Apr 09 2014