cp's OEIS Frontend

A208859 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.

%I A208859 #9 Jul 07 2018 06:18:54
%S A208859 5,127,5796,273049,12883280,607924387,28686344276,1353633375649,
%T A208859 63874412830520,3014066220322507,142225889552418956,
%U A208859 6711267165754821049,316687117317930292160,14943635501046735026227,705151014286332805949636
%N A208859 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 A208859 Column 3 of A208864.
%H A208859 R. H. Hardin, <a href="/A208859/b208859.txt">Table of n, a(n) for n = 1..210</a>
%F A208859 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 A208859 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 A208859 Some solutions for n=4:
%e A208859 ..0..1..1....0..1..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
%e A208859 ..0..1..0....0..2..2....0..1..1....0..1..1....0..1..1....0..1..1....1..1..1
%e A208859 ..0..1..2....1..2..1....0..1..2....2..1..2....1..2..0....2..1..2....0..2..0
%e A208859 ..3..2..1....1..3..2....2..0..2....0..2..1....1..0..1....2..1..2....0..1..0
%Y A208859 Cf. A208864.
%K A208859 nonn
%O A208859 1,1
%A A208859 _R. H. Hardin_, Mar 02 2012