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Number of black-square subarrays of (n+2)X(4+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero
2

%I #4 Nov 01 2013 18:11:01

%S 8,48,232,1242,6896,37984,208172,1142054,6269172,34409586,188850410,

%T 1036485334,5688689754,31221981876,171359511448,940494098820,

%U 5161833500756,28330347062146,155489043088298,853390273229980

%N Number of black-square subarrays of (n+2)X(4+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero

%C Column 4 of A230935

%H R. H. Hardin, <a href="/A230931/b230931.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) +a(n-2) +11*a(n-3) -a(n-4) -33*a(n-5) -82*a(n-6) +a(n-7) -33*a(n-8) +71*a(n-9) +125*a(n-10) +117*a(n-11) +140*a(n-12) +66*a(n-13) +35*a(n-14) +2*a(n-15) -4*a(n-16) -4*a(n-17)

%e Some solutions for n=4

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 01 2013