%I #7 Aug 10 2018 09:14:41

%S 64,320,844,1692,2856,4326,6102,8184,10572,13266,16266,19572,23184,

%T 27102,31326,35856,40692,45834,51282,57036,63096,69462,76134,83112,

%U 90396,97986,105882,114084,122592,131406,140526,149952,159684,169722,180066,190716

%N Number of 0..n arrays of length 7 with each element differing from at least one neighbor by 1 or less, starting with 0.

%C Row 7 of A221683.

%H R. H. Hardin, <a href="/A221686/b221686.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 153*n^2 - 213*n + 96 for n>3.

%F Conjectures from _Colin Barker_, Aug 10 2018: (Start)

%F G.f.: 2*x*(32 + 64*x + 38*x^2 + 28*x^3 - 4*x^4 - 5*x^5) / (1 - x)^3.

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

%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 ..1....0....1....0....0....1....0....1....0....0....0....0....0....0....1....1

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

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

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

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

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

%Y Cf. A221683.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 22 2013