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A255105 Number of length n+6 0..2 arrays with at most one downstep in every 6 consecutive neighbor pairs.

%I A255105 #6 Jul 23 2025 15:07:54
%S A255105 540,1008,2032,4338,9297,19263,38010,73278,143045,288057,594045,
%T A255105 1228136,2495244,4970793,9823140,19533636,39362880,80112560,163010352,
%U A255105 329127561,659192991,1316427636,2637095196,5313657069,10747592751,21727946097
%N A255105 Number of length n+6 0..2 arrays with at most one downstep in every 6 consecutive neighbor pairs.
%C A255105 Column 6 of A255107
%H A255105 R. H. Hardin, <a href="/A255105/b255105.txt">Table of n, a(n) for n = 1..210</a>
%F A255105 Empirical: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +25*a(n-6) -42*a(n-7) +18*a(n-8) -10*a(n-12) +6*a(n-13)
%e A255105 Some solutions for n=4
%e A255105 ..0....1....0....1....1....0....2....0....1....2....1....1....0....1....0....0
%e A255105 ..2....0....0....2....1....0....0....1....0....0....1....1....0....1....1....1
%e A255105 ..0....0....2....0....2....0....1....1....0....0....2....0....0....1....2....1
%e A255105 ..0....1....2....0....0....1....1....0....0....0....1....0....1....2....0....0
%e A255105 ..1....1....2....0....0....1....2....0....0....0....1....1....1....1....0....0
%e A255105 ..2....1....0....1....1....0....2....0....0....0....1....2....1....1....0....1
%e A255105 ..2....1....0....2....1....0....2....0....1....0....1....2....2....1....0....1
%e A255105 ..2....1....1....2....1....0....2....1....2....1....1....2....2....1....1....2
%e A255105 ..2....1....1....0....1....1....0....1....2....0....1....0....1....2....2....2
%e A255105 ..0....2....2....0....2....2....0....2....0....0....0....1....2....2....1....1
%Y A255105 Cf. A255107
%K A255105 nonn
%O A255105 1,1
%A A255105 _R. H. Hardin_, Feb 14 2015