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A221520 Number of 0..4 arrays of length n with each element differing from at least one neighbor by 2 or more. 1

%I #12 Oct 18 2017 11:50:52

%S 0,12,30,144,536,2172,8544,33960,134480,533248,2113456,8377808,

%T 33207936,131632288,521770784,2068227136,8198158272,32496344448,

%U 128810916224,510588286464,2023899853184,8022453208832,31799871553536,126050200002816

%N Number of 0..4 arrays of length n with each element differing from at least one neighbor by 2 or more.

%C Column 4 of A221524.

%H R. H. Hardin, <a href="/A221520/b221520.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: 2*x^2*(6 + 3*x + 6*x^2 - 2*x^3 + 4*x^4) / (1 - 2*x - 6*x^2 - 6*x^3 - 4*x^4 - 4*x^6). - _Colin Barker_, Oct 18 2017

%e Some solutions for n=6:

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

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

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

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

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

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

%Y Cf. A221524.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 19 2013

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