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A198900 Number of n X 2 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor.

%I A198900 #8 Feb 18 2018 14:58:25
%S A198900 1,4,33,380,4801,62004,804833,10459180,135958401,1767426404,
%T A198900 22976444833,298693487580,3883014452801,50479185229204,
%U A198900 656229400008033,8530982176189580,110902768218720001,1441735986628126404
%N A198900 Number of n X 2 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor.
%C A198900 Column 2 of A198906.
%H A198900 R. H. Hardin, <a href="/A198900/b198900.txt">Table of n, a(n) for n = 1..200</a>
%F A198900 Empirical: a(n) = 17*a(n-1) -55*a(n-2) +39*a(n-3).
%F A198900 Conjectures from _Colin Barker_, Feb 18 2018: (Start)
%F A198900 G.f.: x*(1 - 13*x + 20*x^2) / ((1 - x)*(1 - 3*x)*(1 - 13*x)).
%F A198900 a(n) = (26 + 13*3^n + 13^n) / 78.
%F A198900 (End)
%e A198900 Some solutions with values 0 to 4 for n=4:
%e A198900 ..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
%e A198900 ..2..3....2..3....2..0....1..2....1..0....2..3....2..3....2..3....1..2....2..3
%e A198900 ..4..2....1..4....3..2....3..1....2..3....1..4....3..1....4..2....2..3....4..0
%e A198900 ..2..4....3..2....4..3....2..4....4..2....4..3....4..2....2..0....4..0....0..3
%K A198900 nonn
%O A198900 1,2
%A A198900 _R. H. Hardin_, Oct 31 2011