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%I A221685 #7 Aug 10 2018 09:14:27
%S A221685 32,113,241,418,636,891,1182,1509,1872,2271,2706,3177,3684,4227,4806,
%T A221685 5421,6072,6759,7482,8241,9036,9867,10734,11637,12576,13551,14562,
%U A221685 15609,16692,17811,18966,20157,21384,22647,23946,25281,26652,28059,29502,30981
%N 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.
%C A221685 Row 6 of A221683.
%H A221685 R. H. Hardin, <a href="/A221685/b221685.txt">Table of n, a(n) for n = 1..210</a>
%F A221685 Empirical: a(n) = 18*n^2 + 57*n - 99 for n>4.
%F A221685 Conjectures from _Colin Barker_, Aug 10 2018: (Start)
%F A221685 G.f.: x*(32 + 17*x - 2*x^2 + 2*x^3 - 8*x^4 - 4*x^5 - x^6) / (1 - x)^3.
%F A221685 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
%F A221685 (End)
%e A221685 Some solutions for n=6:
%e A221685 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A221685 ..1....0....0....1....1....0....1....0....1....0....0....0....1....0....1....0
%e A221685 ..3....0....2....5....0....6....3....0....0....1....5....6....0....1....4....4
%e A221685 ..4....0....1....5....3....5....4....1....5....5....4....6....0....3....4....5
%e A221685 ..3....0....4....2....2....1....2....2....4....4....3....1....2....2....0....2
%e A221685 ..2....1....4....2....2....2....3....1....4....3....2....1....3....3....0....3
%Y A221685 Cf. A221683.
%K A221685 nonn
%O A221685 1,1
%A A221685 _R. H. Hardin_, Jan 22 2013

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