%I #7 Jan 24 2019 08:20:53
%S 14,164,804,2648,6890,15324,30464,55664,95238,154580,240284,360264,
%T 523874,742028,1027320,1394144,1858814,2439684,3157268,4034360,
%U 5096154,6370364,7887344,9680208,11784950,14240564,17089164,20376104,24150098
%N Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by other than one.
%H R. H. Hardin, <a href="/A269539/b269539.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = n^5 + 5*n^4 + 4*n^3 + 6*n^2 - 2*n.
%F Conjectures from _Colin Barker_, Jan 24 2019: (Start)
%F G.f.: 2*x*(7 + 40*x + 15*x^2 + 2*x^3 - 4*x^4) / (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>6.
%F (End)
%e Some solutions for n=3:
%e ..1. .1. .2. .1. .0. .3. .2. .1. .2. .3. .1. .2. .3. .2. .0. .1
%e ..2. .0. .1. .0. .1. .1. .1. .3. .3. .1. .3. .0. .3. .3. .2. .2
%e ..0. .2. .2. .1. .0. .1. .0. .2. .1. .0. .1. .3. .0. .0. .3. .1
%e ..1. .2. .3. .2. .3. .2. .0. .2. .1. .1. .3. .0. .3. .3. .2. .3
%e ..0. .1. .2. .3. .3. .3. .1. .3. .0. .0. .0. .0. .2. .3. .3. .3
%Y Row 5 of A269537.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 29 2016