A221575 - OEIS

%I #8 Aug 08 2018 18:36:55

%S 6,57,342,1293,3734,8991,19014,36497,64998,109059,174326,267669,

%T 397302,572903,805734,1108761,1496774,1986507,2596758,3348509,4265046,

%U 5372079,6697862,8273313,10132134,12310931,14849334,17790117,21179318,25066359

%N Number of 0..n arrays of length 5 with each element differing from at least one neighbor by something other than 1.

%C Row 5 of A221573.

%H R. H. Hardin, <a href="/A221575/b221575.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 1*n^5 + 1*n^4 - 2*n^3 + 12*n^2 - 15*n + 9 for n>2.

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

%F G.f.: x*(6 + 21*x + 90*x^2 - 24*x^3 + 56*x^4 - 39*x^5 + 12*x^6 - 2*x^7) / (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>8.

%F (End)

%e Some solutions for n=6:

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

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

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

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

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

%Y Cf. A221573.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 20 2013