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%I #8 Aug 17 2018 09:21:39
%S 5,114,4865,213469,9383963,412602889,18142309235,797728639489,
%T 35076656042963,1542343995891289,67817897342466755,
%U 2981998328788355809,131120462107713937763,5765454466967090614489,253510891259359153159475
%N Number of n X 3 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order.
%C Column 3 of A223062.
%H R. H. Hardin, <a href="/A223057/b223057.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 55*a(n-1) - 515*a(n-2) + 1337*a(n-3) - 696*a(n-4) - 1188*a(n-5) + 1008*a(n-6) for n>7.
%F Empirical g.f.: x*(5 - 161*x + 1170*x^2 - 2081*x^3 - 295*x^4 + 2238*x^5 - 336*x^6) / ((1 - x)*(1 - 2*x)*(1 - 52*x + 357*x^2 - 162*x^3 - 504*x^4)). - _Colin Barker_, Aug 17 2018
%e Some solutions for n=3:
%e ..0..1..1....0..1..1....0..1..2....0..1..0....0..1..0....0..1..2....0..1..0
%e ..2..2..0....0..2..3....0..2..3....0..2..1....2..0..2....1..0..1....0..2..0
%e ..3..3..2....3..2..1....1..1..2....1..0..3....1..3..2....3..2..2....2..1..2
%Y Cf. A223062.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 13 2013
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