%I
%S 243,622,1137,1905,2951,4338,6141,8448,11361,14997,19489,24987,31659,
%T 39692,49293,60690,74133,89895,108273,129589,154191,182454,214781,
%U 251604,293385,340617,393825,453567,520435,595056,678093,770246,872253,984891
%N Number of length n+4 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.
%C Row 4 of A255107.
%H R. H. Hardin, <a href="/A255111/b255111.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/120)*n^5 + (7/24)*n^4 + (85/24)*n^3 + (1505/24)*n^2 + (2809/20)*n + 30 for n>2.
%F Empirical g.f.: x*(243  836*x + 1050*x^2  447*x^3  219*x^4 + 339*x^5  156*x^6 + 27*x^7) / (1  x)^6.  _Colin Barker_, Jan 24 2018
%e Some solutions for n=4:
%e 1 1 0 0 2 2 1 2 0 0 2 2 1 2 0 0
%e 1 1 0 2 0 0 2 0 0 2 2 2 2 0 1 2
%e 1 2 0 1 1 0 2 2 2 1 2 2 0 0 1 1
%e 0 2 1 1 1 0 1 2 2 1 2 2 0 0 2 2
%e 0 2 2 1 1 1 2 2 2 1 1 2 2 0 2 2
%e 0 2 2 2 2 2 2 2 2 2 1 1 2 1 0 2
%e 1 2 0 0 1 2 2 0 2 2 2 1 2 2 2 2
%e 0 2 0 0 1 2 0 2 0 2 2 2 1 1 2 0
%Y Cf. A255107.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 14 2015
