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A221678 Number of 0..3 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0. 1

%I

%S 0,2,5,20,68,241,844,2966,10413,36568,128408,450913,1583400,5560186,

%T 19524853,68562444,240760252,845440977,2968805844,10425101678,

%U 36608235997,128551546480,451414815600,1585164405441,5566379537040

%N Number of 0..3 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.

%C Column 3 of A221683.

%H R. H. Hardin, <a href="/A221678/b221678.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x^2*(2 - x + x^2) / ((1 + x)*(1 - 4*x + 2*x^2 - x^3)). - _Colin Barker_, Oct 19 2017

%e Some solutions for n=6

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

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

%e ..1....2....0....1....0....1....3....1....1....2....0....2....0....1....3....2

%e ..0....1....2....2....2....3....2....1....2....3....1....0....2....2....2....3

%e ..0....2....3....1....3....3....1....1....1....3....0....0....1....1....3....2

%e ..0....2....3....2....3....3....2....2....1....2....1....0....0....0....3....1

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 22 2013

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Last modified January 27 19:55 EST 2023. Contains 359847 sequences. (Running on oeis4.)