A189348 - OEIS

%I #8 May 02 2018 09:23:03

%S 1,4,13,45,160,565,2005,7108,25209,89401,317056,1124425,3987721,

%T 14142276,50154949,177872293,630816160,2237161405,7933993245,

%U 28137553540,99788579953,353895752689,1255075518976,4451069407761,15785519335825

%N Number of n X 2 array permutations with each element moving one space diagonally, horizontally or vertically.

%C Column 2 of A189355.

%H R. H. Hardin, <a href="/A189348/b189348.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 3*a(n-1) +3*a(n-2) -3*a(n-3) -3*a(n-4) +a(n-5).

%F Empirical g.f.: x*(1 + x - 2*x^2 - 3*x^3 + x^4) / ((1 - x)*(1 - 2*x - 5*x^2 - 2*x^3 + x^4)). - _Colin Barker_, May 02 2018

%e Some solutions for 3 X 2:

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

%e ..0..5....3..1....5..1....4..5....3..5....4..1....4..2....5..0....0..2....3..2

%e ..2..4....5..4....2..4....2..3....2..4....5..2....5..3....2..4....5..4....5..4

%Y Cf. A189355.

%K nonn

%O 1,2

%A _R. H. Hardin_, Apr 20 2011