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A258729 Number of length n+7 0..3 arrays with at most one downstep in every 7 consecutive neighbor pairs.

%I A258729 #6 Jul 23 2025 15:31:27
%S A258729 5115,10280,22866,55660,138196,331584,752180,1607656,3343894,7100132,
%T A258729 15867680,37057120,87647408,203774064,457583316,996246248,2145967651,
%U A258729 4684383672,10501666108,24080284440,55579151729,126886388888
%N A258729 Number of length n+7 0..3 arrays with at most one downstep in every 7 consecutive neighbor pairs.
%C A258729 Column 7 of A258730
%H A258729 R. H. Hardin, <a href="/A258729/b258729.txt">Table of n, a(n) for n = 1..210</a>
%F A258729 Empirical: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4) +116*a(n-7) -303*a(n-8) +268*a(n-9) -80*a(n-10) -206*a(n-14) +320*a(n-15) -125*a(n-16) +20*a(n-21) -10*a(n-22)
%e A258729 Some solutions for n=4
%e A258729 ..0....3....1....1....1....2....3....1....2....0....3....1....3....1....2....0
%e A258729 ..0....0....2....1....0....1....0....0....2....2....3....1....1....2....2....0
%e A258729 ..3....1....2....0....0....1....0....1....2....2....0....1....2....0....2....2
%e A258729 ..1....1....1....0....1....1....0....1....2....1....0....1....2....0....1....2
%e A258729 ..1....2....2....0....2....2....0....1....3....1....0....0....2....0....1....0
%e A258729 ..1....2....2....2....2....2....0....3....3....1....2....0....2....0....2....1
%e A258729 ..1....2....2....2....3....2....0....3....0....1....2....0....2....0....2....2
%e A258729 ..2....2....2....2....3....2....2....3....1....2....3....0....3....0....2....2
%e A258729 ..2....3....2....2....2....2....2....2....3....3....3....2....0....1....3....2
%e A258729 ..3....3....3....2....2....3....3....2....3....3....3....3....0....0....3....2
%e A258729 ..2....0....1....0....3....1....3....3....3....0....1....3....1....0....0....3
%Y A258729 Cf. A258730
%K A258729 nonn
%O A258729 1,1
%A A258729 _R. H. Hardin_, Jun 08 2015