A208859 - OEIS

%I #9 Jul 07 2018 06:18:54

%S 5,127,5796,273049,12883280,607924387,28686344276,1353633375649,

%T 63874412830520,3014066220322507,142225889552418956,

%U 6711267165754821049,316687117317930292160,14943635501046735026227,705151014286332805949636

%N Number of n X 3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or left-upward diagonal neighbors.

%C Column 3 of A208864.

%H R. H. Hardin, <a href="/A208859/b208859.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 59*a(n-1) - 603*a(n-2) + 2211*a(n-3) - 2826*a(n-4) + 720*a(n-5) for n>6.

%F Empirical g.f.: x*(5 - 168*x + 1318*x^2 - 3389*x^3 + 1710*x^4 - 240*x^5) / ((1 - 2*x)*(1 - 57*x + 489*x^2 - 1233*x^3 + 360*x^4)). - _Colin Barker_, Jul 07 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A208864.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 02 2012