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 A221512 Number of 0..5 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 13:28:18

%S 0,4,13,80,381,1970,9940,50495,255980,1298632,6586395,33407907,

%T 169448914,859472004,4359369001,22111382192,112152257687,568853184739,

%U 2885309153794,14634723355722,74229524701062,376503348140640

%N Number of 0..5 arrays of length n with each element differing from at least one neighbor by 2 or more, starting with 0.

%C Column 5 of A221515.

%H R. H. Hardin, <a href="/A221512/b221512.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +11*a(n-2) +20*a(n-3) +17*a(n-4) -3*a(n-5) +a(n-6).

%F Empirical g.f.: x^2*(4 + 5*x + 10*x^2 - 2*x^3) / (1 - 2*x - 11*x^2 - 20*x^3 - 17*x^4 + 3*x^5 - 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 ..2....2....4....5....2....3....3....4....3....5....2....3....3....3....2....5

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 18 2013

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Last modified April 20 17:12 EDT 2024. Contains 371845 sequences. (Running on oeis4.)