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Number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock having zero permanent.
1

%I #8 Jun 14 2018 11:35:39

%S 361,8029,99856,1718209,26512201,434613664,6990799321,113636628469,

%T 1841188465216,29885540089249,484822312979761,7867521981505504,

%U 127659187514359081,2071519703855856109,33613908262858076176

%N Number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock having zero permanent.

%C Column 2 of A206255.

%H R. H. Hardin, <a href="/A206249/b206249.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 19*a(n-1) - 855*a(n-3) + 2025*a(n-4).

%F Empirical g.f.: x*(361 + 1170*x - 52695*x^2 + 129600*x^3) / ((1 - 19*x + 45*x^2)*(1 - 45*x^2)). - _Colin Barker_, Jun 14 2018

%e Some solutions for n=4:

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

%e ..0..0..0....0..0..0....1..0..1....0..0..1....0..0..0....0..0..0....0..0..0

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

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

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

%Y Cf. A206255.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 05 2012