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A230703 Number of (n+3) X (3+3) 0..2 white square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

%I A230703 #6 Apr 12 2023 08:04:26
%S A230703 30,244,2106,16536,130446,1025430,8053490,63237238,496590056,
%T A230703 3899177780,30617038898,240407287782,1887698838680,14822368917190,
%U A230703 116386479715646,913876264039036,7175832414626878,56345230976142602,442427428831168274
%N A230703 Number of (n+3) X (3+3) 0..2 white square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.
%C A230703 Column 3 of A230708.
%H A230703 R. H. Hardin, <a href="/A230703/b230703.txt">Table of n, a(n) for n = 1..210</a>
%F A230703 Empirical: a(n) = 6*a(n-1) +27*a(n-2) -64*a(n-3) -295*a(n-4) -13*a(n-5) +1890*a(n-6) +812*a(n-7) -4466*a(n-8) -467*a(n-9) -3948*a(n-10) +16934*a(n-11) -22529*a(n-12) +17109*a(n-13) -1911*a(n-14) -6225*a(n-15) +731*a(n-16) +3024*a(n-17) -978*a(n-18) -86*a(n-19) +436*a(n-20) -24*a(n-21) -30*a(n-22).
%e A230703 Some solutions for n=2
%e A230703 ..0..x..0..x..0..x....0..x..2..x..2..x....0..x..0..x..1..x....0..x..0..x..2..x
%e A230703 ..x..1..x..1..x..2....x..1..x..0..x..2....x..1..x..2..x..0....x..1..x..0..x..1
%e A230703 ..0..x..2..x..1..x....0..x..1..x..0..x....0..x..2..x..1..x....2..x..0..x..1..x
%e A230703 ..x..1..x..0..x..1....x..2..x..0..x..1....x..1..x..0..x..1....x..0..x..2..x..0
%e A230703 ..0..x..0..x..2..x....1..x..2..x..2..x....0..x..0..x..2..x....2..x..1..x..2..x
%Y A230703 Cf. A230708.
%K A230703 nonn
%O A230703 1,1
%A A230703 _R. H. Hardin_, Oct 28 2013