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A208085 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.

%I A208085 #8 Apr 20 2013 08:18:40
%S A208085 8,20,12,56,20,24,164,32,56,36,488,52,134,60,72,1460,84,344,96,168,
%T A208085 108,4376,136,888,156,402,180,216,13124,220,2318,252,1032,288,504,324,
%U A208085 39368,356,6056,408,2664,468,1206,540,648,118100,576,15848,660,6954,756,3096
%N A208085 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.
%C A208085 Table starts
%C A208085 ...8..20...56..164..488..1460..4376..13124..39368.118100..354296.1062884
%C A208085 ..12..20...32...52...84...136...220....356....576....932....1508....2440
%C A208085 ..24..56..134..344..888..2318..6056..15848..41478.108584..284264..744206
%C A208085 ..36..60...96..156..252...408...660...1068...1728...2796....4524....7320
%C A208085 ..72.168..402.1032.2664..6954.18168..47544.124434.325752..852792.2232618
%C A208085 .108.180..288..468..756..1224..1980...3204...5184...8388...13572...21960
%C A208085 .216.504.1206.3096.7992.20862.54504.142632.373302.977256.2558376.6697854
%C A208085 .324.540..864.1404.2268..3672..5940...9612..15552..25164...40716...65880
%H A208085 R. H. Hardin, <a href="/A208085/b208085.txt">Table of n, a(n) for n = 1..5596</a>
%F A208085 Empirical for column k:
%F A208085 k=1: a(n) = 3*a(n-2)
%F A208085 k=2..7: a(n) = 3*a(n-2) for n>3
%F A208085 Empirical for row n:
%F A208085 n=1: a(k)=4*a(k-1)-3*a(k-2)
%F A208085 n=2,4,6: a(k)=a(k-1)+a(k-2)
%F A208085 n=3,5,7: a(k)=3*a(k-1)-3*a(k-3)+a(k-4)
%e A208085 Some solutions for n=4 k=3
%e A208085 ..0..1..0..0....0..1..0..1....0..0..0..0....0..1..1..1....0..0..0..0
%e A208085 ..0..1..0..1....0..0..0..0....1..1..1..1....0..1..0..1....1..0..1..0
%e A208085 ..1..0..1..0....0..0..0..0....1..1..1..1....1..0..1..0....0..1..0..1
%e A208085 ..1..0..1..0....1..0..1..0....1..0..1..0....1..0..1..0....0..0..0..0
%e A208085 ..0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1....0..0..0..0
%Y A208085 Column 1 is A153339(n+2).
%Y A208085 Row 1 is A115099.
%Y A208085 Row 2 is A022087(n+3).
%Y A208085 Row 4 is A022346(n+3).
%K A208085 nonn,tabl
%O A208085 1,1
%A A208085 _R. H. Hardin_ Feb 23 2012