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A221679 Number of 0..4 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0. 1

%I

%S 0,2,5,26,100,418,1692,6932,28288,115604,472188,1929012,7880012,

%T 32190588,131500508,537189116,2194454252,8964498844,36620598988,

%U 149597691420,611116954220,2496455194876,10198192807820,41660325742812

%N Number of 0..4 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.

%C Column 4 of A221683.

%H R. H. Hardin, <a href="/A221679/b221679.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x^2*(2 - x + 3*x^2 + 2*x^3 + 2*x^4) / (1 - 3*x - 4*x^2 - 6*x^4 - 4*x^5 - 4*x^6). - _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 ..1....0....0....0....0....1....1....1....1....0....0....0....1....0....1....1

%e ..0....2....1....0....3....3....0....1....4....4....1....4....3....3....3....2

%e ..2....2....2....3....4....2....2....0....4....3....2....4....2....3....3....4

%e ..2....4....4....2....4....0....3....3....2....0....1....2....0....0....2....4

%e ..2....4....3....2....3....0....2....2....3....1....1....2....1....1....1....3

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 22 2013

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Last modified January 30 16:32 EST 2023. Contains 359945 sequences. (Running on oeis4.)