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A258727 Number of length n+5 0..3 arrays with at most one downstep in every 5 consecutive neighbor pairs.

%I A258727 #6 Jul 23 2025 15:31:14
%S A258727 1212,2936,7834,21860,59188,149960,370510,941024,2487276,6650600,
%T A258727 17371025,44270908,112541478,290771496,762899717,1998910152,
%U A258727 5175319416,13289503784,34202437664,88756842476,231356200114,601422231744
%N A258727 Number of length n+5 0..3 arrays with at most one downstep in every 5 consecutive neighbor pairs.
%C A258727 Column 5 of A258730
%H A258727 R. H. Hardin, <a href="/A258727/b258727.txt">Table of n, a(n) for n = 1..210</a>
%F A258727 Empirical: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4) +52*a(n-5) -128*a(n-6) +108*a(n-7) -31*a(n-8) -68*a(n-10) +92*a(n-11) -31*a(n-12) +4*a(n-15) -a(n-16)
%e A258727 Some solutions for n=4
%e A258727 ..0....1....1....0....1....0....1....3....3....2....1....1....1....3....3....1
%e A258727 ..2....3....2....3....0....1....0....3....0....2....1....3....1....0....0....1
%e A258727 ..0....0....0....3....2....3....0....3....0....2....0....0....1....0....0....2
%e A258727 ..0....0....1....3....2....0....1....3....0....2....0....0....1....1....1....3
%e A258727 ..0....1....1....0....3....0....1....1....0....2....1....1....0....3....1....1
%e A258727 ..0....2....1....1....3....1....2....1....3....3....2....1....2....3....1....1
%e A258727 ..2....3....3....1....0....2....0....2....1....0....3....3....2....0....1....1
%e A258727 ..3....1....0....2....2....2....0....2....1....2....1....1....2....1....1....3
%e A258727 ..0....1....3....3....2....3....2....2....3....3....1....1....3....2....3....3
%Y A258727 Cf. A258730
%K A258727 nonn
%O A258727 1,1
%A A258727 _R. H. Hardin_, Jun 08 2015