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A230068 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j).

%I A230068 #6 Jun 02 2025 08:41:12
%S A230068 0,0,0,0,9,0,0,9,9,0,0,81,45,81,0,0,225,441,441,225,0,0,1089,3645,
%T A230068 15129,3645,1089,0,0,3969,31329,281961,281961,31329,3969,0,0,16641,
%U A230068 266805,6487209,14082255,6487209,266805,16641,0,0,65025,2277081,137945025
%N A230068 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j).
%C A230068 Table starts
%C A230068 .0.....0.......0..........0.............0................0...................0
%C A230068 .0.....9.......9.........81...........225.............1089................3969
%C A230068 .0.....9......45........441..........3645............31329..............266805
%C A230068 .0....81.....441......15129........281961..........6487209...........137945025
%C A230068 .0...225....3645.....281961......14082255........793041921.........43142680647
%C A230068 .0..1089...31329....6487209.....793041921.....114228452529......15615593045649
%C A230068 .0..3969..266805..137945025...43142680647...15615593045649....5392746297039195
%C A230068 .0.16641.2277081.3020271849.2369158188849.2168295406671681.1888668174848027049
%H A230068 R. H. Hardin, <a href="/A230068/b230068.txt">Table of n, a(n) for n = 1..312</a>
%F A230068 Empirical for column k:
%F A230068 k=1: a(n) = a(n-1)
%F A230068 k=2: a(n) = 3*a(n-1) +6*a(n-2) -8*a(n-3)
%F A230068 k=3: a(n) = 7*a(n-1) +14*a(n-2) -8*a(n-3)
%F A230068 k=4: [order 10] for n>11
%F A230068 k=5: [order 16] for n>19
%e A230068 Some solutions for n=4 k=4
%e A230068 ..0..1..2..0....1..1..1..0....1..2..1..2....0..0..0..2....0..1..0..1
%e A230068 ..1..2..2..0....1..1..2..1....1..1..0..0....2..2..0..2....2..2..1..2
%e A230068 ..1..2..0..1....2..2..0..1....1..1..2..2....0..0..2..2....0..0..1..1
%e A230068 ..0..1..1..2....0..0..1..2....1..0..1..0....2..2..0..0....2..1..1..1
%Y A230068 Column 2 is A208556(n-2)
%K A230068 nonn,tabl
%O A230068 1,5
%A A230068 _R. H. Hardin_, Oct 08 2013