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A221521 Number of 0..5 arrays of length n with each element differing from at least one neighbor by 2 or more. 1

%I #9 Oct 18 2017 13:28:47

%S 0,20,68,400,1940,9982,50400,256018,1297924,6584320,33394958,

%T 169387004,859152000,4357755890,22103183110,112110699524,568642349004,

%U 2884239836106,14629299498936,74202014273586,376363810775194

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

%C Column 5 of A221524.

%H R. H. Hardin, <a href="/A221521/b221521.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.: 2*x^2*(10 + 14*x + 22*x^2 - 4*x^3 + x^4) / (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 ..2....4....0....4....2....0....0....5....2....1....2....0....0....0....4....5

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

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 19 2013

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Last modified July 16 11:34 EDT 2024. Contains 374347 sequences. (Running on oeis4.)