A241133 - OEIS

%I #9 Oct 29 2018 20:15:58

%S 1,2,5,17,56,195,691,2476,8941,32393,117632,427635,1555643,5661060,

%T 20604893,75004865,273044808,994013923,3618750915,13174348572,

%U 47962513037,174612764153,635697854288,2314333217939,8425607885003

%N Number of n X 2 0..2 arrays with no element equal to the same number of vertical neighbors as horizontal neighbors, with new values 0..2 introduced in row major order.

%H R. H. Hardin, <a href="/A241133/b241133.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + 2*a(n-2) - 11*a(n-3) - 6*a(n-4) + 8*a(n-5) for n>6.

%F Empirical g.f.: x*(1 - x)*(1 - x - 6*x^2 - 2*x^3 + 4*x^4) / ((1 - 2*x)*(1 - 2*x - 6*x^2 - x^3 + 4*x^4)). - _Colin Barker_, Oct 29 2018

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A241138.

%K nonn

%O 1,2

%A _R. H. Hardin_, Apr 16 2014