A232951 - OEIS

%I #7 Oct 06 2018 09:39:15

%S 27,771,22971,685251,20442651,609853251,18193384251,542752261251,

%T 16191600916251,483034266181251,14410069980856251,429886928094781251,

%U 12824557492939156251,382587290147700781251,11413495916966327656251

%N Number of n X 4 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

%H R. H. Hardin, <a href="/A232951/b232951.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 31*a(n-1) - 35*a(n-2) + 5*a(n-3).

%F Conjectures from _Colin Barker_, Oct 06 2018: (Start)

%F G.f.: 3*x*(9 - 22*x + 5*x^2) / ((1 - x)*(1 - 30*x + 5*x^2)).

%F a(n) = (55 + (15-2*sqrt(55))^n*(55+sqrt(55)) - (-55+sqrt(55))*(15+2*sqrt(55))^n)/55.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Column 4 of A232955.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 02 2013