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A221514 Number of 0..7 arrays of length n with each element differing from at least one neighbor by 2 or more, starting with 0. 1

%I

%S 0,6,31,252,1765,12872,92934,672526,4864004,35184566,254499831,

%T 1840896185,13315870072,96318591951,696707724524,5039542943168,

%U 36452864937683,263676961336509,1907272308179486,13796001136950442

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

%C Column 7 of A221515.

%H R. H. Hardin, <a href="/A221514/b221514.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.: x^2*(6 + 13*x + 33*x^2 + 10*x^3 + 13*x^4 - 4*x^5 + 4*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 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

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

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 18 2013

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Last modified June 2 11:35 EDT 2020. Contains 334771 sequences. (Running on oeis4.)