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A209650 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically.

%I A209650 #7 Jul 22 2025 21:52:47
%S A209650 2,4,4,6,16,6,9,36,36,8,14,81,102,64,10,22,196,270,216,100,12,35,484,
%T A209650 798,630,390,144,14,56,1225,2354,2156,1215,636,196,16,90,3136,7210,
%U A209650 7128,4690,2079,966,256,18,145,8100,22232,24990,16830,8904,3276,1392,324,20,234
%N A209650 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically.
%C A209650 Table starts
%C A209650 ..2...4....6....9....14.....22.....35......56.......90......145.......234
%C A209650 ..4..16...36...81...196....484...1225....3136.....8100....21025.....54756
%C A209650 ..6..36..102..270...798...2354...7210...22232....69570...218950....693810
%C A209650 ..8..64..216..630..2156...7128..24990...87136...311040..1112150...4018716
%C A209650 .10.100..390.1215..4690..16830..65765..251160...994050..3911375..15639390
%C A209650 .12.144..636.2079..8904..34012.145775..597856..2579940.10954895..47622744
%C A209650 .14.196..966.3276.15386..61754.287140.1247736..5805450.26247900.122620446
%C A209650 .16.256.1392.4860.24808.103664.518700.2364992.11769120.56106300.279344520
%H A209650 R. H. Hardin, <a href="/A209650/b209650.txt">Table of n, a(n) for n = 1..2828</a>
%F A209650 Empirical for column k:
%F A209650 k=1: a(n) = 2*n
%F A209650 k=2: a(n) = 4*n^2
%F A209650 k=3: a(n) = 2*n^3 + 6*n^2 - 2*n
%F A209650 k=4: a(n) = 9*n^3 + (9/2)*n^2 - (9/2)*n
%F A209650 k=5: a(n) = (7/2)*n^4 + 21*n^3 - (7/2)*n^2 - 7*n
%F A209650 k=6: a(n) = 22*n^4 + (88/3)*n^3 - 22*n^2 - (22/3)*n
%F A209650 k=7: a(n) = 7*n^5 + 70*n^4 + (35/3)*n^3 - (105/2)*n^2 - (7/6)*n
%e A209650 Some solutions for n=4 k=3
%e A209650 ..1..1..1....1..1..1....1..1..0....0..0..0....0..1..0....0..0..0....0..1..0
%e A209650 ..1..1..1....1..1..1....1..1..0....0..1..1....1..1..0....0..0..0....0..0..0
%e A209650 ..1..1..1....0..1..0....1..1..0....0..1..0....0..0..0....0..0..0....0..0..0
%e A209650 ..1..1..1....0..1..0....1..1..0....0..0..0....0..0..0....0..0..0....0..0..0
%Y A209650 Column 2 is A016742
%Y A209650 Column 3 is A086113
%Y A209650 Row 1 is A001611(n+2)
%Y A209650 Row 2 is A207436
%Y A209650 Row 3 is A207747
%K A209650 nonn,tabl
%O A209650 1,1
%A A209650 _R. H. Hardin_ Mar 11 2012