%I
%S 81,216,441,789,1302,2032,3042,4407,6215,8568,11583,15393,20148,26016,
%T 33184,41859,52269,64664,79317,96525,116610,139920,166830,197743,
%U 233091,273336,318971,370521,428544,493632,566412,647547,737737,837720,948273
%N Number of length n+3 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.
%C Row 3 of A255107.
%H R. H. Hardin, <a href="/A255110/b255110.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/120)*n^5 + (1/4)*n^4 + (59/24)*n^3 + (93/4)*n^2 + (1321/30)*n + 11.
%F Empirical g.f.: x*(81  270*x + 360*x^2  237*x^3 + 78*x^4  11*x^5) / (1  x)^6.  _Colin Barker_, Jan 24 2018
%e Some solutions for n=4:
%e 1 0 2 0 2 0 2 0 2 0 2 0 1 0 0 0
%e 0 2 1 1 0 0 2 2 0 0 0 2 1 0 1 0
%e 0 0 1 1 0 0 2 1 0 0 0 1 2 0 0 0
%e 0 0 1 1 1 0 2 2 1 0 1 1 0 0 0 1
%e 1 1 1 2 1 0 0 2 1 0 1 2 2 1 0 2
%e 1 2 0 0 2 1 0 2 1 0 0 2 2 2 0 2
%e 1 1 2 1 2 2 2 1 2 0 2 1 2 2 0 0
%Y Cf. A255107.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 14 2015
