%I #7 Jan 21 2018 09:37:29
%S 16,32,64,128,245,442,753,1220,1894,2836,4118,5824,8051,10910,14527,
%T 19044,24620,31432,39676,49568,61345,75266,91613,110692,132834,158396,
%U 187762,221344,259583,302950,351947,407108,469000,538224,615416,701248
%N Number of length n+3 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.
%C Row 3 of A256816.
%H R. H. Hardin, <a href="/A256818/b256818.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/120)*n^5 + (1/12)*n^4 + (31/24)*n^3  (31/12)*n^2 + (66/5)*n + 4.
%F Empirical g.f.: x*(16  64*x + 112*x^2  96*x^3 + 37*x^4  4*x^5) / (1  x)^6.  _Colin Barker_, Jan 21 2018
%e Some solutions for n=4:
%e ..0....1....1....1....1....1....1....0....0....1....0....1....0....1....1....0
%e ..1....1....1....1....1....1....0....1....0....0....1....0....0....1....1....1
%e ..1....1....1....1....1....1....1....0....1....1....0....0....0....0....0....0
%e ..0....0....1....0....1....0....1....1....1....1....0....1....0....1....1....1
%e ..1....0....0....1....1....1....0....1....1....1....1....0....1....0....0....0
%e ..0....0....0....0....1....1....0....1....0....0....0....1....1....0....1....1
%e ..0....1....0....1....1....1....0....0....0....1....0....1....0....0....0....0
%Y Cf. A256816.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 10 2015
