A200833 - OEIS

%I #11 Oct 14 2017 10:45:48

%S 56,194,676,2356,8210,28610,99700,347434,1210736,4219166,14702926,

%T 51236674,178549274,622207508,2168265232,7555958512,26330961818,

%U 91757987972,319757721532,1114289913490,3883071237050,13531704854780

%N Number of 0..3 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.

%C Column 3 of A200838.

%H R. H. Hardin, <a href="/A200833/b200833.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: 2*x*(28 - 15*x + 6*x^2 - 8*x^3) / (1 - 4*x + 2*x^2 - x^3 + x^4). - _Colin Barker_, Oct 14 2017

%e Some solutions for n=3

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Nov 23 2011