A258726 - OEIS

%I #4 Jun 08 2015 11:49:54

%S 512,1408,4184,12549,35540,98676,281136,819453,2358888,6678576,

%T 18944656,54386801,156395364,446683118,1271579860,3632749828,

%U 10409795664,29790138680,85049570304,242860722210,694569186912,1987109647472

%N Number of length n+4 0..3 arrays with at most one downstep in every 4 consecutive neighbor pairs

%C Column 4 of A258730

%H R. H. Hardin, <a href="/A258726/b258726.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) +30*a(n-4) -72*a(n-5) +58*a(n-6) -16*a(n-7) -31*a(n-8) +36*a(n-9) -10*a(n-10) +a(n-12)

%e Some solutions for n=4

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

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

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

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

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

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

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

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

%Y Cf. A258730

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 08 2015