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A230176 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally, vertically, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

%I A230176 #6 Jun 02 2025 08:41:55
%S A230176 0,3,3,3,27,3,9,193,193,9,15,1407,3787,1407,15,33,10211,78849,78849,
%T A230176 10211,33,63,73417,1637019,4722977,1637019,73417,63,129,530771,
%U A230176 33908253,284444079,284444079,33908253,530771,129,255,3841171,704822331
%N A230176 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally, vertically, diagonally or antidiagonally next to at least one element with value 2-x(i,j).
%C A230176 Table starts
%C A230176 ...0.......3...........3..............9.................15
%C A230176 ...3......27.........193...........1407..............10211
%C A230176 ...3.....193........3787..........78849............1637019
%C A230176 ...9....1407.......78849........4722977..........284444079
%C A230176 ..15...10211.....1637019......284444079........49754476927
%C A230176 ..33...73417....33908253....17072965263......8666440899433
%C A230176 ..63..530771...704822331..1027868078181...1514677019365483
%C A230176 .129.3841171.14643857893.61861526624839.264644708761844781
%H A230176 R. H. Hardin, <a href="/A230176/b230176.txt">Table of n, a(n) for n = 1..112</a>
%F A230176 Empirical for column k:
%F A230176 k=1: a(n) = a(n-1) +2*a(n-2)
%F A230176 k=2: a(n) = 6*a(n-1) -2*a(n-2) +67*a(n-3) +62*a(n-4) +160*a(n-5) +40*a(n-6) +16*a(n-7)
%F A230176 k=3: [order 26] for n>27
%F A230176 k=4: [order 81] for n>82
%e A230176 Some solutions for n=3 k=4
%e A230176 ..1..1..0..1....0..2..1..1....2..1..2..0....2..0..1..2....1..1..2..0
%e A230176 ..0..0..1..2....0..0..2..1....0..0..1..0....1..1..0..1....0..1..1..2
%e A230176 ..2..1..1..0....0..2..0..0....2..0..1..1....0..2..1..1....1..2..1..1
%Y A230176 Column 1 is A062510(n-1)
%K A230176 nonn,tabl
%O A230176 1,2
%A A230176 _R. H. Hardin_, Oct 11 2013