login
Number of n X 3 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.
1

%I #8 Jun 29 2018 08:35:40

%S 4,25,161,1033,6631,42563,273205,1753657,11256431,72253147,463780861,

%T 2976931745,19108426759,122653794067,787294181189,5053509615817,

%U 32437632650335,208211736387083,1336476297041869,8578617726111793

%N Number of n X 3 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.

%C Column 3 of A208269.

%H R. H. Hardin, <a href="/A208264/b208264.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) + 3*a(n-2) - 2*a(n-3).

%F Empirical g.f.: x*(4 + x - x^2) / (1 - 6*x - 3*x^2 + 2*x^3). - _Colin Barker_, Jun 29 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A208269.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 24 2012