A221574 - OEIS

%I #8 Aug 08 2018 15:19:04

%S 2,9,26,59,114,197,314,471,674,929,1242,1619,2066,2589,3194,3887,4674,

%T 5561,6554,7659,8882,10229,11706,13319,15074,16977,19034,21251,23634,

%U 26189,28922,31839,34946,38249,41754,45467,49394,53541,57914,62519,67362

%N Number of 0..n arrays of length 3 with each element differing from at least one neighbor by something other than 1.

%C Row 3 of A221573.

%H R. H. Hardin, <a href="/A221574/b221574.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 1*n^3 - 1*n^2 + 3*n - 1.

%F Conjectures from _Colin Barker_, Aug 08 2018: (Start)

%F G.f.: x*(2 + x)*(1 + x^2) / (1 - x)^4.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3.

%F (End)

%e Some solutions for n=6:

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

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

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

%Y Cf. A221573.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 20 2013