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A229847 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally or vertically next to at least one element with value 2-x(i,j).

%I A229847 #7 Jun 02 2025 08:39:25
%S A229847 0,3,3,3,15,3,9,81,81,9,15,423,987,423,15,33,2247,13401,13401,2247,33,
%T A229847 63,11925,178311,453837,178311,11925,63,129,63291,2381469,15269193,
%U A229847 15269193,2381469,63291,129,255,335943,31783299,514371027,1296261759,514371027
%N A229847 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally or vertically next to at least one element with value 2-x(i,j).
%C A229847 Table starts
%C A229847 ...0......3.........3............9..............15..................33
%C A229847 ...3.....15........81..........423............2247...............11925
%C A229847 ...3.....81.......987........13401..........178311.............2381469
%C A229847 ...9....423.....13401.......453837........15269193...........514371027
%C A229847 ..15...2247....178311.....15269193......1296261759........110203382331
%C A229847 ..33..11925...2381469....514371027....110203382331......23643209345079
%C A229847 ..63..63291..31783299..17324310663...9366963651897....5071373978989773
%C A229847 .129.335943.424240833.583513743897.796197119067381.1087831682400037245
%H A229847 R. H. Hardin, <a href="/A229847/b229847.txt">Table of n, a(n) for n = 1..112</a>
%F A229847 Empirical for column k:
%F A229847 k=1: a(n) = a(n-1) +2*a(n-2)
%F A229847 k=2: a(n) = 5*a(n-1) +2*a(n-2) -a(n-3) -5*a(n-4)
%F A229847 k=3: [order 15]
%F A229847 k=4: [order 53]
%e A229847 Some solutions for n=3 k=4
%e A229847 ..0..1..2..0....1..1..0..1....1..1..2..0....1..1..1..1....1..1..1..2
%e A229847 ..2..1..1..1....2..2..2..1....1..2..1..1....1..0..2..0....0..2..0..0
%e A229847 ..1..1..2..0....0..0..2..1....1..0..0..2....0..2..1..1....2..1..1..1
%Y A229847 Column 1 is A062510(n-1)
%K A229847 nonn,tabl
%O A229847 1,2
%A A229847 _R. H. Hardin_, Oct 01 2013