A197244 - OEIS

%I #8 May 11 2018 15:25:30

%S 2,4,8,16,40,80,192,400,936,1984,4576,9824,22408,48560,109888,239728,

%T 539432,1182432,2649952,5828544,13024648,28717648,64040768,141448528,

%U 314965928,696544000,1549366240,3429474848,7622621832,16883244016

%N Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,0,1,1,1 for x=0,1,2,3,4.

%C Every 0 is next to 0 0's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's.

%C Column 2 of A197250.

%H R. H. Hardin, <a href="/A197244/b197244.txt">Table of n, a(n) for n = 1..200</a>

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

%F Empirical g.f.: 2*x*(1 - x)*(1 + x)^3 / (1 - 4*x^2 - 2*x^3 - x^4 + 2*x^5). - _Colin Barker_, May 11 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A197250.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 12 2011