A221610 - OEIS

%I #8 Aug 09 2018 15:12:58

%S 0,2,10,53,269,1378,7057,36152,185192,948664,4859596,24893585,

%T 127518875,653222944,3346172776,17140965623,87805597652,449789301892,

%U 2304071965189,11802743188937,60460241206049,309711116141929,1586513277940591

%N Number of 2 X n arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor, without move-in move-out left turns.

%C Row 2 of A221609.

%H R. H. Hardin, <a href="/A221610/b221610.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) - 9*a(n-2) - 5*a(n-3) + 10*a(n-4) - 3*a(n-5) for n>7.

%F Empirical g.f.: x^2*(1 - x - x^2)*(2 - 2*x + x^2 - 3*x^3) / (1 - 7*x + 9*x^2 + 5*x^3 - 10*x^4 + 3*x^5). - _Colin Barker_, Aug 09 2018

%e Some solutions for n=3:

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

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

%Y Cf. A221609.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 20 2013