A241345 - OEIS

%I #13 Oct 30 2018 05:20:26

%S 1,2,5,22,103,519,2656,13798,72005,377132,1978263,10387415,54569162,

%T 286758658,1507147669,7922014506,41642626111,218903934463,

%U 1150737770732,6049275496670,31800411817677,167171979847160,878810026664375

%N Number of n X 2 0..3 arrays with no element equal to the same number of vertical neighbors as horizontal neighbors, with new values 0..3 introduced in row major order.

%H R. H. Hardin, <a href="/A241345/b241345.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) - 8*a(n-2) - 48*a(n-3) + 59*a(n-4) + 102*a(n-5) - 77*a(n-6) - 112*a(n-7) + 38*a(n-8) + 66*a(n-9) - 27*a(n-10) for n>11.

%F Empirical g.f.: x*(1 - 6*x - 3*x^2 + 46*x^3 + 4*x^4 - 109*x^5 - 38*x^6 + 104*x^7 + 31*x^8 - 51*x^9 + 9*x^10) / ((1 - x)*(1 - 3*x)*(1 - x - 2*x^2 - x^3 + x^4)*(1 - 3*x - 12*x^2 - x^3 + 9*x^4)). - _Colin Barker_, Oct 30 2018

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A241349.

%K nonn

%O 1,2

%A _R. H. Hardin_, Apr 19 2014