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A221523 Number of 0..7 arrays of length n with each element differing from at least one neighbor by 2 or more. 1

%I

%S 0,42,222,1764,12458,90684,654864,4738970,34274630,247928860,

%T 1793345580,12971955294,93830864024,678713206224,4909381705850,

%U 35511361462492,256866719859442,1858011331955384,13439678399558656,97214130194552336

%N Number of 0..7 arrays of length n with each element differing from at least one neighbor by 2 or more.

%C Column 7 of A221524.

%H R. H. Hardin, <a href="/A221523/b221523.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +21*a(n-2) +58*a(n-3) +79*a(n-4) +32*a(n-5) +23*a(n-6) +4*a(n-7) +8*a(n-8).

%F Empirical g.f.: 2*x^2*(21 + 48*x + 108*x^2 + 34*x^3 + 36*x^4 + 12*x^6) / (1 - 3*x - 21*x^2 - 58*x^3 - 79*x^4 - 32*x^5 - 23*x^6 - 4*x^7 - 8*x^8). _Colin Barker_, Oct 18 2017

%e Some solutions for n=6

%e ..5....1....3....1....0....6....4....5....2....7....5....7....1....0....0....0

%e ..3....4....7....6....3....3....6....2....5....3....0....5....6....4....3....4

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

%e ..6....0....1....1....0....4....7....2....2....5....6....7....3....7....7....2

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

%e ..4....6....2....7....0....0....3....6....2....5....0....7....6....5....3....1

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 19 2013

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Last modified June 26 16:55 EDT 2022. Contains 354885 sequences. (Running on oeis4.)