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Half the number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock diagonal sum differing from its antidiagonal sum by more than 3.
1

%I #8 Apr 12 2018 09:04:31

%S 57,411,2318,14641,88103,541936,3302001,20204829,123402988,754319381,

%T 4609217629,28168842830,172139309061,1051973256999,6428702835542,

%U 39286618550317,240084864227147,1467186858794824,8966146857909117

%N Half the number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock diagonal sum differing from its antidiagonal sum by more than 3.

%C Column 2 of A184231.

%H R. H. Hardin, <a href="/A184224/b184224.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 6*a(n-1) + 7*a(n-2) - 42*a(n-3) + 17*a(n-4) + 24*a(n-5) - 12*a(n-6).

%F Empirical g.f.: x*(57 + 69*x - 547*x^2 + 250*x^3 + 324*x^4 - 168*x^5) / (1 - 6*x - 7*x^2 + 42*x^3 - 17*x^4 - 24*x^5 + 12*x^6). - _Colin Barker_, Apr 12 2018

%e Some solutions for 5 X 3:

%e ..0..1..0....3..0..3....0..3..0....2..0..3....2..3..0....3..0..2....2..0..3

%e ..3..0..3....1..3..0....2..0..3....0..3..0....3..0..2....0..3..1....0..3..2

%e ..2..3..1....3..1..3....1..3..0....3..0..2....1..3..1....3..0..3....1..0..3

%e ..3..0..2....0..3..0....2..0..2....0..3..0....3..0..2....1..3..1....0..3..1

%e ..1..3..1....3..1..3....1..3..1....2..0..1....0..2..0....2..0..3....2..0..2

%Y Cf. A184231.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 10 2011