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A255102 Number of length n+3 0..2 arrays with at most one downstep in every 3 consecutive neighbor pairs. 2

%I

%S 66,168,441,1137,2907,7498,19338,49698,127871,329325,847491,2180700,

%T 5613144,14447250,37180603,95692059,246288681,633868172,1631378124,

%U 4198705332,10806224445,27811942767,71579710341,184225016494

%N Number of length n+3 0..2 arrays with at most one downstep in every 3 consecutive neighbor pairs.

%C Column 3 of A255107.

%H R. H. Hardin, <a href="/A255102/b255102.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) -3*a(n-2) +8*a(n-3) -9*a(n-4) +3*a(n-5) -a(n-6).

%F Empirical g.f.: x*(66 - 30*x + 135*x^2 - 210*x^3 + 69*x^4 - 26*x^5) / ((1 - x)*(1 - 2*x + x^2 - 7*x^3 + 2*x^4 - x^5)). - _Colin Barker_, Jan 24 2018

%e Some solutions for n=4:

%e ..0....2....0....2....2....1....0....0....0....2....2....0....0....0....0....2

%e ..1....1....2....1....0....1....2....1....2....2....0....0....1....1....0....0

%e ..0....1....0....1....1....1....0....0....2....2....0....0....1....2....0....0

%e ..2....1....0....1....2....2....1....0....2....2....1....1....0....0....1....1

%e ..2....2....1....1....1....2....1....2....2....2....1....2....0....0....2....0

%e ..1....1....1....1....1....0....0....2....2....2....1....1....0....2....1....0

%e ..2....2....0....0....2....2....1....1....1....1....1....1....1....2....2....1

%Y Cf. A255107.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 14 2015

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Last modified May 16 03:58 EDT 2022. Contains 353688 sequences. (Running on oeis4.)