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A255108 Number of length n+1 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.

%I A255108 #8 Jan 24 2018 16:46:07
%S A255108 9,26,66,147,294,540,927,1507,2343,3510,5096,7203,9948,13464,17901,
%T A255108 23427,30229,38514,48510,60467,74658,91380,110955,133731,160083,
%U A255108 190414,225156,264771,309752,360624,417945,482307,554337,634698,724090,823251,932958
%N A255108 Number of length n+1 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.
%C A255108 Row 1 of A255107.
%H A255108 R. H. Hardin, <a href="/A255108/b255108.txt">Table of n, a(n) for n = 1..210</a>
%F A255108 Empirical: a(n) = (1/120)*n^5 + (1/6)*n^4 + (19/24)*n^3 + (11/6)*n^2 + (16/5)*n + 3.
%F A255108 Empirical g.f.: x*(9 - 28*x + 45*x^2 - 39*x^3 + 17*x^4 - 3*x^5) / (1 - x)^6. - _Colin Barker_, Jan 24 2018
%e A255108 Some solutions for n=4:
%e A255108 ..1....1....0....0....0....1....0....0....1....2....0....0....1....1....0....0
%e A255108 ..1....2....0....0....0....1....1....1....1....1....2....2....2....0....0....0
%e A255108 ..0....0....2....2....1....2....0....1....1....2....2....2....2....0....2....2
%e A255108 ..0....2....1....0....1....2....0....2....1....2....2....1....0....0....2....0
%e A255108 ..1....2....1....2....2....1....1....1....2....2....0....2....2....0....1....1
%Y A255108 Cf. A255107.
%K A255108 nonn
%O A255108 1,1
%A A255108 _R. H. Hardin_, Feb 14 2015