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Number of (n+3)X(2+3) 0..3 black 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
1

%I #4 Nov 03 2013 06:00:23

%S 16,242,724,10534,28128,419878,1144652,16946918,46058744,683352174,

%T 1857863476,27552792942,74908095984,1110991043910,3020446141788,

%U 44796988899478,121789649054696,1806294227298910,4910772371719684

%N Number of (n+3)X(2+3) 0..3 black 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 2 of A231023

%H R. H. Hardin, <a href="/A231020/b231020.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 31*a(n-2) +375*a(n-4) +233*a(n-6) -7946*a(n-8) -884*a(n-10) -16296*a(n-12) -203520*a(n-14) +53120*a(n-16)

%e Some solutions for n=2

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 03 2013