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%I #7 Aug 06 2018 05:35:49
%S 0,5,89,532,1970,5513,12872,26477,49598,86465,142388,223877,338762,
%T 496313,707360,984413,1341782,1795697,2364428,3068405,3930338,4975337,
%U 6231032,7727693,9498350,11578913,14008292,16828517,20084858,23825945
%N Number of 0..n arrays of length 6 with each element differing from at least one neighbor by 2 or more, starting with 0.
%C Row 6 of A221515.
%H R. H. Hardin, <a href="/A221517/b221517.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 1*n^5 - 20*n^3 + 78*n^2 - 146*n + 125 for n>4.
%F Conjectures from _Colin Barker_, Aug 06 2018: (Start)
%F G.f.: x^2*(5 + 59*x + 73*x^2 + 13*x^3 - 32*x^4 + 9*x^5 - 9*x^6 + 3*x^7 - x^8) / (1 - x)^6.
%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>10.
%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 ..3....2....6....3....2....5....3....2....5....3....2....4....3....6....5....3
%e ..5....0....5....5....6....2....0....2....1....0....4....0....4....6....6....2
%e ..5....1....1....4....5....6....5....0....3....5....0....6....0....1....2....5
%e ..3....5....1....2....2....0....1....4....1....0....1....6....6....3....4....1
%e ..0....1....4....6....5....5....5....6....4....3....6....4....4....0....1....5
%Y Cf. A221515.
%K nonn
%O 1,2
%A _R. H. Hardin_, Jan 18 2013
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