%I #7 Jan 21 2018 09:36:46

%S 27,81,243,694,1803,4248,9186,18483,35016,63060,108774,180801,290998,

%T 455313,694827,1036980,1517001,2179563,3080685,4289904,5892741,

%U 7993486,10718328,14218857,18675966,24304182,31356456,40129443,50969304,64278063

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

%C Row 2 of A255622.

%H R. H. Hardin, <a href="/A255624/b255624.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/40320)*n^8 + (13/10080)*n^7 + (59/2880)*n^6 + (61/360)*n^5 + (5167/5760)*n^4 + (901/1440)*n^3 + (17077/3360)*n^2 + (3977/280)*n + 6.

%F Empirical g.f.: x*(3 - 2*x)*(9 - 48*x + 130*x^2 - 195*x^3 + 171*x^4 - 87*x^5 + 24*x^6 - 3*x^7) / (1 - x)^9. - _Colin Barker_, Jan 21 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Cf. A255622.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 28 2015