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A258726 Number of length n+4 0..3 arrays with at most one downstep in every 4 consecutive neighbor pairs.

%I A258726 #6 Jul 23 2025 15:31:07
%S A258726 512,1408,4184,12549,35540,98676,281136,819453,2358888,6678576,
%T A258726 18944656,54386801,156395364,446683118,1271579860,3632749828,
%U A258726 10409795664,29790138680,85049570304,242860722210,694569186912,1987109647472
%N A258726 Number of length n+4 0..3 arrays with at most one downstep in every 4 consecutive neighbor pairs.
%C A258726 Column 4 of A258730
%H A258726 R. H. Hardin, <a href="/A258726/b258726.txt">Table of n, a(n) for n = 1..210</a>
%F A258726 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 A258726 Some solutions for n=4
%e A258726 ..3....3....3....0....1....0....1....0....1....0....2....0....3....1....0....2
%e A258726 ..3....1....3....0....1....0....0....2....0....0....1....1....0....1....2....3
%e A258726 ..1....1....3....1....2....2....0....3....2....0....1....2....0....0....0....0
%e A258726 ..2....2....2....3....3....2....0....0....2....0....2....2....0....2....0....1
%e A258726 ..2....2....2....3....1....2....0....0....2....1....3....0....1....2....0....3
%e A258726 ..2....1....3....0....2....2....2....0....2....3....3....0....2....2....0....3
%e A258726 ..1....1....3....3....2....1....0....0....1....1....3....1....2....0....3....1
%e A258726 ..2....3....2....3....3....2....1....3....2....2....1....1....3....0....1....1
%Y A258726 Cf. A258730
%K A258726 nonn
%O A258726 1,1
%A A258726 _R. H. Hardin_, Jun 08 2015