A208867 - OEIS

%I #9 Jul 07 2018 08:51:31

%S 5,136,6520,324682,16205218,808928836,40380275500,2015711853262,

%T 100620769519078,5022810805035976,250729829501722000,

%U 12515989521112631602,624776054783641480618,31187715359825604175756

%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 right-upward antidiagonal neighbors.

%C Column 3 of A208872.

%H R. H. Hardin, <a href="/A208867/b208867.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 55*a(n-1) -261*a(n-2) +369*a(n-3) -162*a(n-4) for n>5.

%F Empirical g.f.: x*(5 - 139*x + 345*x^2 - 267*x^3 + 54*x^4) / ((1 - x)*(1 - 3*x)*(1 - 51*x + 54*x^2)). - _Colin Barker_, Jul 07 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A208872.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 02 2012