A234780 - OEIS

%I #8 Oct 16 2018 05:42:09

%S 484,6660,91916,1269036,17521780,241927524,3340355564,46121153580,

%T 636806710036,8792555155236,121401086008460,1676216233423404,

%U 23143951620064564,319554533544992100,4412172198832106156

%N Number of (n+1) X (2+1) 0..3 arrays with no adjacent elements equal and with each 2 X 2 subblock having the number of clockwise edge increases equal to the number of counterclockwise edge increases.

%H R. H. Hardin, <a href="/A234780/b234780.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 16*a(n-1) - 31*a(n-2) + 10*a(n-3).

%F Empirical g.f.: 4*x*(121 - 271*x + 90*x^2) / (1 - 16*x + 31*x^2 - 10*x^3). - _Colin Barker_, Oct 16 2018

%e Some solutions for n=3:

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

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

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

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

%Y Column 2 of A234786.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 30 2013