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A221513 Number of 0..6 arrays of length n with each element differing from at least one neighbor by 2 or more, starting with 0. 1

%I

%S 0,5,21,150,884,5513,33860,208756,1285694,7921082,48795589,300602292,

%T 1851824780,11407972817,70277580919,432937512858,2667065000212,

%U 16430167559715,101216282472118,623532037268338,3841202145282104

%N Number of 0..6 arrays of length n with each element differing from at least one neighbor by 2 or more, starting with 0.

%C Column 6 of A221515.

%H R. H. Hardin, <a href="/A221513/b221513.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +14*a(n-2) +29*a(n-3) +28*a(n-4) +a(n-5) +27*a(n-6) +8*a(n-7) +2*a(n-8).

%F Empirical g.f.: x^2*(5 + 6*x + 17*x^2 - 5*x^3 + 12*x^4 + 2*x^5 + 2*x^6) / (1 - 3*x - 14*x^2 - 29*x^3 - 28*x^4 - x^5 - 27*x^6 - 8*x^7 - 2*x^8). - _Colin Barker_, Oct 18 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 ..4....4....3....5....2....6....2....3....4....2....5....4....4....6....5....5

%e ..3....0....0....2....4....1....0....6....4....4....4....0....1....2....5....1

%e ..1....0....4....5....0....4....0....2....0....0....1....3....4....0....2....2

%e ..2....4....0....1....1....3....5....0....4....4....2....5....0....0....3....5

%e ..4....1....3....4....3....5....2....5....0....2....6....0....3....6....0....2

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 18 2013

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Last modified January 23 16:48 EST 2020. Contains 331173 sequences. (Running on oeis4.)