A221894 - OEIS

A221894

Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor, without move-in move-out straight through or left turns.

%I #9 Aug 11 2018 10:45:40

%S 3,31,266,2305,19936,172624,1494152,12933821,111957318,969123166,

%T 8388906524,72615905296,628576515760,5441072941952,47098919537873,

%U 407696835820987,3529098152699791,30548517126329090,264433534642030465

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

%C Column 2 of A221898.

%H R. H. Hardin, <a href="/A221894/b221894.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) + 26*a(n-2) + 45*a(n-3) + 34*a(n-4) - 2*a(n-5) - 4*a(n-6) + a(n-7).

%F Empirical g.f.: x*(3 + 16*x + 33*x^2 + 34*x^3 - 2*x^4 - 4*x^5 + x^6) / (1 - 5*x - 26*x^2 - 45*x^3 - 34*x^4 + 2*x^5 + 4*x^6 - x^7). - _Colin Barker_, Aug 11 2018

%e Some solutions for n=3:

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

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

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

%Y Cf. A221898.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 30 2013