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Number of (n+2)X(3+2) 0..3 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..3 introduced in row major order
1

%I #4 Nov 09 2013 06:20:52

%S 3,8,21,54,185,561,1943,6756,24003,88488,325775,1225789,4623559,

%T 17568716,67018935,256235910,982016953,3767662049,14470021611,

%U 55610192696,213805376253,822314635406,3163303832419,12170737198879,46831328979593

%N Number of (n+2)X(3+2) 0..3 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..3 introduced in row major order

%C Column 3 of A231441

%H R. H. Hardin, <a href="/A231436/b231436.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) +12*a(n-2) -72*a(n-3) -81*a(n-4) +451*a(n-5) +368*a(n-6) -1550*a(n-7) -591*a(n-8) +2319*a(n-9) -679*a(n-10) -285*a(n-11) +4312*a(n-12) -2776*a(n-13) -9014*a(n-14) +6322*a(n-15) +7616*a(n-16) -11742*a(n-17) +4058*a(n-18) +8508*a(n-19) -8690*a(n-20) -710*a(n-21) +2637*a(n-22) -237*a(n-23) -180*a(n-24)

%e Some solutions for n=6

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

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

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 09 2013