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A198901 Number of n X 3 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor.

%I A198901 #8 Mar 02 2018 10:49:53
%S A198901 2,33,1211,50384,2125425,89793204,3794115705,160319061892,
%T A198901 6774239755817,286243775060868,12095158053422201,511077834439270724,
%U A198901 21595464215307153225,912510860892666556164,38557914891188891686425
%N A198901 Number of n X 3 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor.
%C A198901 Column 3 of A198906.
%H A198901 R. H. Hardin, <a href="/A198901/b198901.txt">Table of n, a(n) for n = 1..200</a>
%F A198901 Empirical: a(n) = 51*a(n-1) - 393*a(n-2) + 1013*a(n-3) - 902*a(n-4) + 232*a(n-5).
%F A198901 Empirical g.f.: x*(2 - 69*x + 314*x^2 - 434*x^3 + 139*x^4) / ((1 - x)*(1 - 5*x + 2*x^2)*(1 - 45*x + 116*x^2)). - _Colin Barker_, Mar 02 2018
%e A198901 Some solutions with values 0 to 4 for n=4:
%e A198901 ..0..1..2....0..1..2....0..1..2....0..1..0....0..1..0....0..1..0....0..1..2
%e A198901 ..1..0..3....1..3..1....2..3..1....1..0..2....2..3..2....2..0..3....2..3..1
%e A198901 ..2..1..4....4..1..0....4..0..2....3..4..3....3..2..4....4..2..0....1..4..0
%e A198901 ..4..0..3....2..0..2....0..1..3....1..2..1....2..1..0....3..0..4....3..0..4
%Y A198901 Cf. A198906.
%K A198901 nonn
%O A198901 1,1
%A A198901 _R. H. Hardin_, Oct 31 2011