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Number of (n+3) X (1+3) 0..3 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 4, and upper left element zero.
2

%I #8 Mar 18 2018 05:14:33

%S 6,16,76,314,1170,4584,18208,71242,278758,1094600,4294812,16840082,

%T 66052162,259099696,1016260448,3986056882,15634778470,61325029216,

%U 240537044748,943467829258,3700602618386,14515016732376,56932811822272

%N Number of (n+3) X (1+3) 0..3 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 4, and upper left element zero.

%C Column 1 of A230949.

%H R. H. Hardin, <a href="/A230942/b230942.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + 14*a(n-3) + a(n-4) - a(n-5).

%F Empirical g.f.: 2*x*(3 - x + 14*x^2 + x^3 - x^4) / (1 - 3*x - 14*x^3 - x^4 + x^5). - _Colin Barker_, Mar 18 2018

%e Some solutions for n=2:

%e ..0..x..0..x....0..x..2..x....0..x..0..x....0..x..0..x....0..x..0..x

%e ..x..1..x..3....x..1..x..3....x..1..x..1....x..1..x..1....x..1..x..3

%e ..2..x..2..x....0..x..0..x....0..x..2..x....2..x..2..x....0..x..2..x

%e ..x..3..x..1....x..3..x..3....x..3..x..1....x..3..x..1....x..1..x..1

%e ..2..x..0..x....2..x..2..x....2..x..0..x....2..x..0..x....0..x..0..x

%Y Cf. A230949.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 01 2013