A208170 - OEIS

%I #8 Jun 29 2018 06:03:00

%S 5,159,8469,473928,26625693,1496307201,84091222866,4725865313907,

%T 265590215430897,14925978329967384,838829205068709369,

%U 47141595663874099773,2649323638611897879018,148890075596000256587991

%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 neighbors.

%C Column 3 of A208175.

%H R. H. Hardin, <a href="/A208170/b208170.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 62*a(n-1) - 333*a(n-2) + 396*a(n-3) - 135*a(n-4) for n>5.

%F Empirical g.f.: x*(5 - 151*x + 276*x^2 - 183*x^3 + 45*x^4) / ((1 - 5*x + 3*x^2)*(1 - 57*x + 45*x^2)). - _Colin Barker_, Jun 29 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A208175.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 24 2012