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A255106 Number of length n+7 0..2 arrays with at most one downstep in every 7 consecutive neighbor pairs.

%I A255106 #6 Jul 23 2025 15:08:00
%S A255106 927,1616,3042,6141,12662,25578,49611,91887,166290,303969,573853,
%T A255106 1118256,2210103,4340001,8343339,15695433,29216435,54612816,103548108,
%U A255106 199304393,386593848,747736983,1432037309,2714684340,5119381929,9669662693
%N A255106 Number of length n+7 0..2 arrays with at most one downstep in every 7 consecutive neighbor pairs.
%C A255106 Column 7 of A255107
%H A255106 R. H. Hardin, <a href="/A255106/b255106.txt">Table of n, a(n) for n = 1..210</a>
%F A255106 Empirical: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +33*a(n-7) -57*a(n-8) +25*a(n-9) -15*a(n-14) +10*a(n-15)
%e A255106 Some solutions for n=4
%e A255106 ..0....2....1....0....0....2....1....0....0....0....0....0....1....1....0....0
%e A255106 ..1....2....1....0....2....2....1....1....0....1....1....1....0....2....0....0
%e A255106 ..1....1....1....0....0....1....1....2....0....0....2....2....0....2....1....0
%e A255106 ..1....2....0....1....0....1....1....0....0....0....2....0....1....2....1....0
%e A255106 ..2....2....1....1....1....1....1....0....0....0....0....0....1....2....0....1
%e A255106 ..2....2....1....1....1....1....2....0....1....1....0....0....1....2....0....1
%e A255106 ..2....2....1....1....2....1....0....0....1....1....0....0....1....0....0....2
%e A255106 ..1....2....2....1....2....1....1....0....1....2....0....0....1....2....0....2
%e A255106 ..1....2....2....1....2....1....1....0....0....2....1....1....2....2....0....2
%e A255106 ..1....2....2....1....2....2....1....0....2....1....2....2....0....2....1....2
%e A255106 ..2....0....0....1....0....0....2....1....2....2....2....1....2....2....1....1
%Y A255106 Cf. A255107
%K A255106 nonn
%O A255106 1,1
%A A255106 _R. H. Hardin_, Feb 14 2015