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%I #8 Jan 24 2018 14:25:42
%S 294,597,1302,2951,6582,14001,29147,61542,133392,292534,634197,
%T 1353282,2874273,6149472,13283988,28746325,61881375,132509427,
%U 283590718,609038592,1311917331,2825639015,6072583563,13028913003,27962048781
%N Number of length n+5 0..2 arrays with at most one downstep in every 5 consecutive neighbor pairs.
%C Column 5 of A255107.
%H R. H. Hardin, <a href="/A255104/b255104.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +18*a(n-5) -29*a(n-6) +12*a(n-7) -6*a(n-10) +3*a(n-11).
%F Empirical g.f.: x*(294 - 285*x + 393*x^2 + 542*x^3 + 1038*x^4 - 3486*x^5 + 1719*x^6 - 129*x^7 - 318*x^8 - 684*x^9 + 441*x^10) / (1 - 3*x + 3*x^2 - x^3 - 18*x^5 + 29*x^6 - 12*x^7 + 6*x^10 - 3*x^11). - _Colin Barker_, Jan 24 2018
%e Some solutions for n=4:
%e ..2....0....0....2....1....1....1....0....0....0....2....1....1....0....2....0
%e ..0....0....1....0....2....1....1....0....0....0....2....1....1....1....0....2
%e ..1....0....1....0....0....0....1....1....1....2....1....2....0....1....0....2
%e ..1....0....2....0....1....0....2....0....1....2....1....0....1....2....1....2
%e ..1....1....0....1....1....1....1....1....1....2....1....1....1....2....1....2
%e ..1....1....2....1....1....1....1....1....1....2....1....2....2....2....1....0
%e ..0....0....2....1....1....2....1....1....1....1....1....2....2....0....0....1
%e ..0....0....2....1....0....1....2....2....1....1....2....2....0....1....0....1
%e ..2....2....2....0....0....1....2....2....1....1....2....0....0....1....0....1
%Y Cf. A255107.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 14 2015
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