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A221511 Number of 0..4 arrays of length n with each element differing from at least one neighbor by 2 or more, starting with 0. 1

%I #9 Oct 18 2017 13:28:01

%S 0,3,7,36,130,532,2088,8304,32876,130376,516704,2048264,8118864,

%T 32182256,127565600,505652480,2004334368,7944899296,31492457536,

%U 124831656000,494815052864,1961376994048,7774621408896,30817501320448,122156223100160

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

%C Column 4 of A221515.

%H R. H. Hardin, <a href="/A221511/b221511.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.: x^2*(3 + x + 4*x^2 - 2*x^3 + 2*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....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

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

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 18 2013

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Last modified February 22 09:38 EST 2024. Contains 370250 sequences. (Running on oeis4.)