A268459 - OEIS

%I #12 Jan 14 2019 03:09:39

%S 16,176,852,2776,7160,15816,31276,56912,97056,157120,243716,364776,

%T 529672,749336,1036380,1405216,1872176,2455632,3176116,4056440,

%U 5121816,6399976,7921292,9718896,11828800,14290016,17144676,20438152,24219176

%N Number of length-5 0..n arrays with no adjacent pair x,x+1 followed at any distance by x+1,x.

%H R. H. Hardin, <a href="/A268459/b268459.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^5 + 5*n^4 + 7*n^3 + n^2 + 2*n.

%F Conjectures from _Colin Barker_, Jan 13 2019: (Start)

%F G.f.: 4*x*(4 + 20*x + 9*x^2 - 4*x^3 + 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=9:

%e   7  5  8  9  3  4  1  2  0  4  3  1  5  1  5  3

%e   1  4  0  0  3  4  6  4  1  4  6  5  9  8  7  0

%e   3  1  2  5  2  7  1  2  3  7  4  6  7  6  6  3

%e   6  1  7  6  1  6  7  1  6  5  4  8  6  6  5  9

%e   1  1  9  6  5  3  5  8  3  6  4  9  4  6  5  7

%Y Row 5 of A268457.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 04 2016