cp's OEIS Frontend

A232950 Number of n X 3 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.

%I A232950 #8 Oct 06 2018 09:39:28
%S A232950 9,129,1881,27441,400329,5840289,85202361,1242993681,18133691049,
%T A232950 264547403649,3859408908441,56303849204721,821401284620169,
%U A232950 11983196174074209,174819534903392121,2550393846506436561
%N A232950 Number of n X 3 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 A232950 R. H. Hardin, <a href="/A232950/b232950.txt">Table of n, a(n) for n = 1..210</a>
%F A232950 Empirical: a(n) = 15*a(n-1) - 6*a(n-2).
%F A232950 Conjectures from _Colin Barker_, Oct 06 2018: (Start)
%F A232950 G.f.: 3*x*(3 - 2*x) / (1 - 15*x + 6*x^2).
%F A232950 a(n) = (2^(-1-n)*((15-sqrt(201))^n*(-3+sqrt(201)) + (3+sqrt(201))*(15+sqrt(201))^n)) / sqrt(201).
%F A232950 (End)
%e A232950 Some solutions for n=4:
%e A232950 ..0..1..3....0..1..0....0..0..0....0..1..3....0..2..0....0..0..0....0..0..0
%e A232950 ..0..2..3....3..2..0....0..1..0....1..1..3....0..1..3....2..2..2....2..0..0
%e A232950 ..2..2..2....0..2..2....0..0..0....0..1..1....1..1..0....2..3..2....2..0..2
%e A232950 ..0..2..3....3..2..3....2..0..0....0..1..1....3..1..3....3..3..2....0..0..2
%Y A232950 Column 3 of A232955.
%K A232950 nonn
%O A232950 1,1
%A A232950 _R. H. Hardin_, Dec 02 2013