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A255103 Number of length n+4 0..2 arrays with at most one downstep in every 4 consecutive neighbor pairs.

%I A255103 #7 Jan 24 2018 19:02:16
%S A255103 147,331,789,1905,4429,10125,23463,55246,129480,300432,696375,1623876,
%T A255103 3795126,8845445,20569653,47880261,111630444,260248590,606129714,
%U A255103 1411326056,3287784315,7661560197,17850285244,41578206276,96850762992
%N A255103 Number of length n+4 0..2 arrays with at most one downstep in every 4 consecutive neighbor pairs.
%C A255103 Column 4 of A255107.
%H A255103 R. H. Hardin, <a href="/A255103/b255103.txt">Table of n, a(n) for n = 1..210</a>
%F A255103 Empirical: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +12*a(n-4) -18*a(n-5) +7*a(n-6) -3*a(n-8) +a(n-9).
%F A255103 Empirical g.f.: x*(147 - 110*x + 237*x^2 + 384*x^3 - 1014*x^4 + 438*x^5 - 69*x^6 - 172*x^7 + 66*x^8) / (1 - 3*x + 3*x^2 - x^3 - 12*x^4 + 18*x^5 - 7*x^6 + 3*x^8 - x^9). - _Colin Barker_, Jan 24 2018
%e A255103 Some solutions for n=4:
%e A255103 ..1....2....1....0....2....0....1....1....1....0....1....0....0....1....0....0
%e A255103 ..1....0....0....0....0....0....2....2....1....1....1....0....0....2....2....1
%e A255103 ..2....1....0....1....0....1....0....1....0....1....0....1....0....1....2....0
%e A255103 ..0....1....0....0....0....0....1....2....0....0....0....1....0....1....2....0
%e A255103 ..0....1....1....1....0....1....1....2....2....1....2....0....2....1....0....1
%e A255103 ..0....1....2....1....2....2....1....2....2....1....2....1....2....2....0....2
%e A255103 ..1....0....2....2....2....2....1....0....2....1....2....1....2....2....0....1
%e A255103 ..1....0....0....1....0....1....2....0....0....0....1....2....2....2....0....2
%Y A255103 Cf. A255107.
%K A255103 nonn
%O A255103 1,1
%A A255103 _R. H. Hardin_, Feb 14 2015