A221689 - OEIS

%I #9 Aug 10 2018 17:33:28

%S 6,152,3112,63676,1302720,26650988,545221260,11154026300,228186749552,

%T 4668196767064,95500991265668,1953739262283024,39969188300499044,

%U 817681276128120100,16727952148700884996,342216938625170086928

%N Number of n X 3 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without consecutive moves in the same direction.

%C Column 3 of A221693.

%H R. H. Hardin, <a href="/A221689/b221689.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 24*a(n-1) - 69*a(n-2) - 71*a(n-3) + 2*a(n-4) for n>5.

%F Empirical g.f.: 2*x*(3 + 4*x - 61*x^2 - 49*x^3 + 2*x^4) / (1 - 24*x + 69*x^2 + 71*x^3 - 2*x^4). - _Colin Barker_, Aug 10 2018

%e Some solutions for n=3:

%e ..0..4..0....0..3..0....0..2..1....0..2..2....0..3..1....1..1..1....1..2..0

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

%e ..1..1..2....2..2..0....2..1..2....1..1..2....2..1..1....0..4..0....0..2..0

%Y Cf. A221693.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 22 2013