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%I #7 Jan 21 2018 09:36:52
%S 81,243,729,2040,5088,11386,23298,44361,79692,136494,224676,357603,
%T 552993,833979,1230355,1780026,2530683,3541725,4886451,6654546,
%U 8954886,11918688,15703032,20494783,26514942,34023456,43324518,54772389,68777775
%N Number of length n+3 0..2 arrays with at most two downsteps in every n consecutive neighbor pairs.
%C Row 3 of A255622.
%H R. H. Hardin, <a href="/A255625/b255625.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/40320)*n^8 + (1/672)*n^7 + (29/960)*n^6 + (39/80)*n^5 + (2463/640)*n^4 + (1/32)*n^3 + (112103/10080)*n^2 + (44923/840)*n + 12.
%F Empirical g.f.: x*(81 - 486*x + 1458*x^2 - 2577*x^3 + 2766*x^4 - 1790*x^5 + 672*x^6 - 135*x^7 + 12*x^8) / (1 - x)^9. - _Colin Barker_, Jan 21 2018
%e Some solutions for n=4:
%e ..2....1....0....0....2....1....1....2....0....0....0....0....1....2....2....0
%e ..1....2....2....0....0....2....2....1....1....0....2....0....1....0....2....1
%e ..1....0....2....2....0....2....0....2....0....0....0....2....1....1....1....2
%e ..0....2....2....1....1....0....0....0....0....0....2....1....1....0....0....0
%e ..2....0....1....2....0....2....1....2....2....0....1....1....0....0....2....1
%e ..2....0....2....1....2....0....1....0....2....1....1....1....2....2....2....1
%e ..0....1....0....2....1....0....1....2....1....1....0....2....0....2....2....0
%Y Cf. A255622.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 28 2015
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