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A255989 Number of length n+5 0..1 arrays with at most one downstep in every 5 consecutive neighbor pairs.

%I A255989 #7 Jan 24 2018 14:03:26
%S A255989 42,68,114,196,337,568,945,1574,2645,4476,7568,12736,21365,35852,
%T A255989 60308,101608,171148,287940,484045,813826,1369115,2304172,3877545,
%U A255989 6523278,10972180,18456064,31049291,52240182,87891550,147861804,248739774
%N A255989 Number of length n+5 0..1 arrays with at most one downstep in every 5 consecutive neighbor pairs.
%C A255989 Column 5 of A255992.
%H A255989 R. H. Hardin, <a href="/A255989/b255989.txt">Table of n, a(n) for n = 1..210</a>
%F A255989 Empirical: a(n) = 2*a(n-1) -a(n-2) +4*a(n-5) -3*a(n-6).
%F A255989 Empirical g.f.: x*(42 - 16*x + 20*x^2 + 36*x^3 + 59*x^4 - 78*x^5) / ((1 + x - x^3)*(1 - 3*x + 4*x^2 - 3*x^3)). - _Colin Barker_, Jan 24 2018
%e A255989 Some solutions for n=4:
%e A255989 ..1....0....1....0....0....1....0....0....0....0....0....0....1....1....0....1
%e A255989 ..1....1....0....1....0....0....0....1....1....0....0....1....1....1....1....0
%e A255989 ..0....1....1....0....1....0....1....0....0....1....0....0....0....0....0....0
%e A255989 ..0....1....1....1....1....0....1....0....0....0....0....0....0....0....0....1
%e A255989 ..1....1....1....1....1....0....1....0....1....0....0....0....0....1....0....1
%e A255989 ..1....1....1....1....1....1....1....0....1....0....0....1....1....1....0....1
%e A255989 ..1....1....0....1....0....1....1....0....1....1....1....1....1....1....1....1
%e A255989 ..0....1....0....0....0....0....0....1....1....1....0....0....1....0....0....1
%e A255989 ..0....1....0....1....0....0....0....0....1....0....0....0....0....1....1....0
%Y A255989 Cf. A255992.
%K A255989 nonn
%O A255989 1,1
%A A255989 _R. H. Hardin_, Mar 13 2015