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A221685 Number of 0..n arrays of length 6 with each element differing from at least one neighbor by 1 or less, starting with 0. 1

%I

%S 32,113,241,418,636,891,1182,1509,1872,2271,2706,3177,3684,4227,4806,

%T 5421,6072,6759,7482,8241,9036,9867,10734,11637,12576,13551,14562,

%U 15609,16692,17811,18966,20157,21384,22647,23946,25281,26652,28059,29502,30981

%N Number of 0..n arrays of length 6 with each element differing from at least one neighbor by 1 or less, starting with 0.

%C Row 6 of A221683.

%H R. H. Hardin, <a href="/A221685/b221685.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 18*n^2 + 57*n - 99 for n>4.

%F Conjectures from _Colin Barker_, Aug 10 2018: (Start)

%F G.f.: x*(32 + 17*x - 2*x^2 + 2*x^3 - 8*x^4 - 4*x^5 - x^6) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.

%F (End)

%e Some solutions for n=6:

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..1....0....0....1....1....0....1....0....1....0....0....0....1....0....1....0

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

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

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

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

%Y Cf. A221683.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 22 2013

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Last modified August 11 15:10 EDT 2022. Contains 356066 sequences. (Running on oeis4.)