cp's OEIS Frontend

A208253 Number of n X 3 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

%I A208253 #9 Jun 29 2018 08:06:46
%S A208253 5,96,2040,43344,920928,19566912,415737216,8833148160,187677464064,
%T A208253 3987573838848,84723785029632,1800122089230336,38247105402593280,
%U A208253 812634365429366784,17266002353004576768,366849901919230820352
%N A208253 Number of n X 3 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.
%C A208253 Column 3 of A208258.
%H A208253 R. H. Hardin, <a href="/A208253/b208253.txt">Table of n, a(n) for n = 1..210</a>
%F A208253 Empirical: a(n) = 22*a(n-1) - 16*a(n-2) for n>3.
%F A208253 Conjectures from _Colin Barker_, Jun 29 2018: (Start)
%F A208253 G.f.: x*(1 - 2*x)*(5 - 4*x) / (1 - 22*x + 16*x^2).
%F A208253 a(n) = (1/32)*sqrt(3/35)*((11-sqrt(105))^n*(-13+sqrt(105)) + (11+sqrt(105))^n*(13+sqrt(105))) for n>1.
%F A208253 (End)
%e A208253 Some solutions for n=4:
%e A208253 ..0..0..1....0..0..0....0..1..0....0..0..1....0..0..0....0..1..2....0..0..1
%e A208253 ..2..0..0....0..1..2....0..1..1....2..0..2....1..2..1....1..2..0....1..1..2
%e A208253 ..2..0..1....2..0..0....1..0..2....0..2..0....0..2..2....0..1..0....1..0..1
%e A208253 ..2..2..2....1..0..1....1..2..0....2..0..2....0..0..2....2..0..1....2..1..2
%Y A208253 Cf. A208258.
%K A208253 nonn
%O A208253 1,1
%A A208253 _R. H. Hardin_, Feb 24 2012