cp's OEIS Frontend

A186161 1/4 the number of n X 2 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

%I A186161 #8 Apr 17 2018 11:24:22
%S A186161 1,7,48,321,2175,14748,99933,677283,4590168,31108893,210834267,
%T A186161 1428886932,9683993481,65631317487,444803049600,3014563174089,
%U A186161 20430595384935,138464249604684,938413592805957,6359909317239723
%N A186161 1/4 the number of n X 2 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.
%C A186161 Column 2 of A186168.
%H A186161 R. H. Hardin, <a href="/A186161/b186161.txt">Table of n, a(n) for n = 1..200</a>
%F A186161 Empirical: a(n) = 5*a(n-1) + 11*a(n-2) + 9*a(n-3) - 9*a(n-4) - 27*a(n-5).
%F A186161 Empirical g.f.: x*(1 + 2*x + 2*x^2 - 5*x^3 - 12*x^4) / (1 - 5*x - 11*x^2 - 9*x^3 + 9*x^4 + 27*x^5). - _Colin Barker_, Apr 17 2018
%e A186161 Some solutions for 4 X 2 with a(1,1)=0:
%e A186161 ..0..0....0..1....0..0....0..0....0..3....0..2....0..0....0..2....0..2....0..0
%e A186161 ..2..2....0..1....2..3....1..1....0..3....0..2....0..2....0..2....0..2....0..0
%e A186161 ..0..2....3..3....2..3....3..3....2..0....0..2....3..2....3..3....1..1....2..2
%e A186161 ..0..0....0..0....1..1....3..3....2..0....0..2....3..3....3..3....1..1....0..0
%Y A186161 Cf. A186168.
%K A186161 nonn
%O A186161 1,2
%A A186161 _R. H. Hardin_, Feb 13 2011