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%I #8 Jun 11 2018 12:33:48
%S 0,272,3272,18652,71630,214724,542850,1211784,2459988,4633800,8215988,
%T 13857668,22413586,34980764,52940510,78003792,112259976,158228928,
%U 218916480,297873260,399256886,527897524,689366810,890050136,1137222300
%N Number of length 8 nonnegative integer arrays starting and ending with 0 with adjacent elements unequal but differing by no more than n.
%C Row 7 of A205341.
%H R. H. Hardin, <a href="/A205345/b205345.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (841/180)*n^6 - (1/3)*n^5 - (19/36)*n^4 + (1/3)*n^3 - (103/90)*n^2 - 3*n.
%F Conjectures from _Colin Barker_, Jun 11 2018: (Start)
%F G.f.: 2*x^2*(136 + 684*x + 730*x^2 + 129*x^3 + 3*x^4) / (1 - x)^7.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%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....3....5....2....2....2....2....3....5....3....1....2....4....2....3....4
%e ..6....7....8....6....3....4....4....4....9....5....2....5....8....6....5....7
%e ..7....8...11....7....4....3....2....7...12....1....0....4....7....4....6....8
%e .10....4....9....6....3....6....7....3....7....2....4....3....3....8....3....7
%e ..6....5....4....4....0....5....3....6....3....7....6....0....1....3....1....8
%e ..5....3....2....3....3....4....4....2....5....2....5....2....5....5....3....3
%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
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