A198901 - OEIS

%I #8 Mar 02 2018 10:49:53

%S 2,33,1211,50384,2125425,89793204,3794115705,160319061892,

%T 6774239755817,286243775060868,12095158053422201,511077834439270724,

%U 21595464215307153225,912510860892666556164,38557914891188891686425

%N 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 Column 3 of A198906.

%H R. H. Hardin, <a href="/A198901/b198901.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 51*a(n-1) - 393*a(n-2) + 1013*a(n-3) - 902*a(n-4) + 232*a(n-5).

%F 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 Some solutions with values 0 to 4 for n=4:

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

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

%e ..2..1..4....4..1..0....4..0..2....3..4..3....3..2..4....4..2..0....1..4..0

%e ..4..0..3....2..0..2....0..1..3....1..2..1....2..1..0....3..0..4....3..0..4

%Y Cf. A198906.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 31 2011