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Number of length n+6 0..1 arrays with at most one downstep in every 6 consecutive neighbor pairs.
1

%I #7 Jan 24 2018 14:52:15

%S 64,98,156,257,428,705,1134,1797,2848,4560,7384,12021,19508,31444,

%T 50432,80828,129904,209549,338650,546939,881612,1418697,2281990,

%U 3673412,5919888,9546459,15393334,24807246,39956320,64344494,103638460,166985169

%N Number of length n+6 0..1 arrays with at most one downstep in every 6 consecutive neighbor pairs.

%C Column 6 of A255992.

%H R. H. Hardin, <a href="/A255990/b255990.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) -a(n-2) +5*a(n-6) -4*a(n-7).

%F Empirical g.f.: x*(64 - 30*x + 24*x^2 + 43*x^3 + 70*x^4 + 106*x^5 - 168*x^6) / (1 - 2*x + x^2 - 5*x^6 + 4*x^7). - _Colin Barker_, Jan 24 2018

%e Some solutions for n=4:

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

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

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

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

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

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

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

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

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

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

%Y Cf. A255992.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 13 2015