%I #9 Jan 21 2018 09:37:00

%S 243,729,2187,5997,14381,30816,60390,110270,190269,313527,497322,

%T 764028,1142238,1668071,2386683,3354003,4638716,6324516,8512653,

%U 11324799,14906259,19429554,25098404,32152140,40870575,51579365,64655892,80535702

%N Number of length n+4 0..2 arrays with at most two downsteps in every n consecutive neighbor pairs.

%C Row 4 of A255622.

%H R. H. Hardin, <a href="/A255626/b255626.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/40320)*n^8 + (17/10080)*n^7 + (119/2880)*n^6 + (871/720)*n^5 + (71047/5760)*n^4 + (3599/1440)*n^3 + (56139/1120)*n^2 + (27661/280)*n + 45 for n>2.

%F Empirical g.f.: x*(243 - 1458*x + 4374*x^2 - 7854*x^3 + 8522*x^4 - 5193*x^5 + 1134*x^6 + 680*x^7 - 630*x^8 + 210*x^9 - 27*x^10) / (1 - x)^9. - _Colin Barker_, Jan 21 2018

%e Some solutions for n=4:

%e ..0....0....1....0....0....2....2....0....1....0....2....1....1....2....2....0

%e ..1....1....1....2....0....2....0....2....0....0....0....0....0....0....2....0

%e ..2....1....2....2....0....0....2....1....0....1....1....1....2....0....0....0

%e ..1....2....1....2....2....1....0....2....1....0....2....2....1....0....2....2

%e ..2....2....1....0....2....1....2....0....1....0....2....0....1....2....0....2

%e ..2....2....2....0....1....2....0....0....2....0....0....1....2....0....2....0

%e ..2....2....2....2....1....0....1....0....2....1....0....2....2....1....2....2

%e ..0....1....2....1....0....2....2....1....0....0....0....0....0....2....1....0

%Y Cf. A255622.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 28 2015