%I #8 Jun 11 2018 13:13:36

%S 0,24,138,454,1130,2370,4424,7588,12204,18660,27390,38874,53638,72254,

%T 95340,123560,157624,198288,246354,302670,368130,443674,530288,629004,

%U 740900,867100,1008774,1167138,1343454,1539030,1755220,1993424,2255088

%N Number of length 6 nonnegative integer arrays starting and ending with 0 with adjacent elements unequal but differing by no more than n.

%C Row 5 of A205341.

%H R. H. Hardin, <a href="/A205343/b205343.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (23/12)*n^4 - (1/2)*n^3 + (1/12)*n^2 - (3/2)*n.

%F Conjectures from _Colin Barker_, Jun 11 2018: (Start)

%F G.f.: 2*x^2*(12 + 9*x + 2*x^2) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

%F (End)

%e Some solutions for n=5:

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

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

%e ..1....2....2....9....5....7....6....6....2....6....0....2....2....0....6....5

%e ..5....0....5....8....1....3....7....8....6....4....5....0....1....2....9....9

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

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%Y Cf. A205341.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 26 2012