A230800 - OEIS

A230800

Number of n X 2 0..3 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, and upper left element zero.

%I #8 Mar 17 2018 05:46:20

%S 0,2,2,16,34,154,432,1618,5058,17664,57586,195866,648928,2185122,

%T 7284482,24435056,81651394,273490714,914714512,3062116338,10245066178,

%U 34289257824,114738331026,383986878106,1284957453248,4300144520002

%N Number of n X 2 0..3 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, and upper left element zero.

%C Column 2 of A230805.

%H R. H. Hardin, <a href="/A230800/b230800.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 6*a(n-2) - 5*a(n-3).

%F Empirical g.f.: 2*x^2*(1 - x) / (1 - 2*x - 6*x^2 + 5*x^3). - _Colin Barker_, Mar 17 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A230805.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 30 2013