A255989 - OEIS

%I #7 Jan 24 2018 14:03:26

%S 42,68,114,196,337,568,945,1574,2645,4476,7568,12736,21365,35852,

%T 60308,101608,171148,287940,484045,813826,1369115,2304172,3877545,

%U 6523278,10972180,18456064,31049291,52240182,87891550,147861804,248739774

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

%C Column 5 of A255992.

%H R. H. Hardin, <a href="/A255989/b255989.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) -a(n-2) +4*a(n-5) -3*a(n-6).

%F 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 Some solutions for n=4:

%e ..1....0....1....0....0....1....0....0....0....0....0....0....1....1....0....1

%e ..1....1....0....1....0....0....0....1....1....0....0....1....1....1....1....0

%e ..0....1....1....0....1....0....1....0....0....1....0....0....0....0....0....0

%e ..0....1....1....1....1....0....1....0....0....0....0....0....0....0....0....1

%e ..1....1....1....1....1....0....1....0....1....0....0....0....0....1....0....1

%e ..1....1....1....1....1....1....1....0....1....0....0....1....1....1....0....1

%e ..1....1....0....1....0....1....1....0....1....1....1....1....1....1....1....1

%e ..0....1....0....0....0....0....0....1....1....1....0....0....1....0....0....1

%e ..0....1....0....1....0....0....0....0....1....0....0....0....0....1....1....0

%Y Cf. A255992.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 13 2015