A265987 - OEIS

%I #8 Jan 09 2019 05:38:42

%S 2,2,6,10,30,66,182,442,1166,2930,7590,19306,49662,126882,325526,

%T 833050,2135150,5467346,14007942,35877322,91909086,235418370,

%U 603054710,1544728186,3956947022,10135859762,25963647846,66507086890,170361678270

%N Number of n X 3 integer arrays with each element equal to the number of horizontal and antidiagonal neighbors not equal to itself.

%H R. H. Hardin, <a href="/A265987/b265987.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3).

%F Conjectures from _Colin Barker_, Jan 09 2019: (Start)

%F G.f.: 2*x*(1 + x)*(1 - 2*x) / ((1 - x)*(1 - x - 4*x^2)).

%F a(n) = 1 + (-((1-sqrt(17))/2)^n + ((1+sqrt(17))/2)^n) / sqrt(17).

%F (End)

%e Some solutions for n=4:

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

%e ..2..4..2....1..1..1....0..0..0....2..4..2....2..4..1....2..1..1....2..4..1

%e ..2..4..2....2..4..2....0..0..0....1..1..1....2..1..1....1..4..2....1..1..1

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

%Y Column 3 of A265991.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 19 2015