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%I #8 Jan 20 2018 12:32:06
%S 729,2187,6561,17622,40659,83325,156563,275166,458604,731981,1127139,
%T 1683927,2451654,3490746,4874628,6691853,9048501,12070872,15908498,
%U 20737500,26764317,34229835,43413945,54640560,68283122,84770631
%N Number of length n+5 0..2 arrays with at most two downsteps in every n consecutive neighbor pairs.
%C Row 5 of A255622.
%H R. H. Hardin, <a href="/A255627/b255627.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/40320)*n^8 + (19/10080)*n^7 + (31/576)*n^6 + (122/45)*n^5 + (188527/5760)*n^4 + (32263/1440)*n^3 + (276001/672)*n^2 - (152493/280)*n + 387 for n>3.
%F Empirical g.f.: x*(729 - 4374*x + 13122*x^2 - 23931*x^3 + 26403*x^4 - 15630*x^5 + 2474*x^6 + 1593*x^7 + 693*x^8 - 1849*x^9 + 924*x^10 - 153*x^11) / (1 - x)^9. - _Colin Barker_, Jan 20 2018
%e Some solutions for n=4:
%e ..0....2....2....2....0....0....2....2....1....2....0....1....2....1....0....0
%e ..2....1....2....0....0....0....0....0....1....1....1....1....1....2....2....1
%e ..0....0....1....0....0....0....1....2....0....1....2....1....0....2....2....0
%e ..1....1....1....2....0....1....1....1....1....2....0....2....1....2....2....1
%e ..1....1....2....2....1....0....2....1....0....0....2....1....1....1....0....1
%e ..0....0....1....1....1....2....2....0....0....2....0....1....0....0....1....0
%e ..1....2....0....2....1....0....1....1....0....0....2....0....0....0....2....0
%e ..1....2....0....2....1....2....1....0....0....0....0....2....0....0....1....1
%e ..0....1....2....1....2....0....0....1....0....0....1....0....1....2....2....1
%Y Cf. A255622.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 28 2015
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