A221821 - OEIS

%I #9 Aug 11 2018 07:11:05

%S 3,31,252,2113,17684,147920,1237439,10351593,86594795,724396370,

%T 6059833949,50692672540,424062286786,3547432284249,29675536361423,

%U 248246446379403,2076670068892280,17372085836189001,145323694322280832

%N Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without consecutive moves in the same direction.

%C Column 2 of A221824.

%H R. H. Hardin, <a href="/A221821/b221821.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*a(n-1) - 4*a(n-2) - 11*a(n-3) - 2*a(n-4) + 22*a(n-5) - 16*a(n-6) + 8*a(n-7).

%F Empirical g.f.: x*(3 + 4*x - 15*x^2 + 2*x^3 + 22*x^4 - 16*x^5 + 8*x^6) / (1 - 9*x + 4*x^2 + 11*x^3 + 2*x^4 - 22*x^5 + 16*x^6 - 8*x^7). - _Colin Barker_, Aug 11 2018

%e Some solutions for n=3:

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

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

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

%Y Cf. A221824.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 26 2013