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%I #9 Jun 06 2018 12:02:56
%S 127,1925,12492,51945,164255,431445,991152,2057553,3945655,7098949,
%T 12120428,19806969,31187079,47562005,70550208,102135201,144716751,
%U 201165445,274880620,369851657,490722639,642860373,832425776,1066448625
%N Number of length 8 nonnegative integer arrays starting and ending with 0 with adjacent elements differing by no more than n.
%C Row 7 of A204213.
%H R. H. Hardin, <a href="/A204216/b204216.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (841/180)*n^6 + (101/5)*n^5 + (1325/36)*n^4 + (73/2)*n^3 + (946/45)*n^2 + (34/5)*n + 1.
%F Conjectures from _Colin Barker_, Jun 06 2018: (Start)
%F G.f.: x*(127 + 1036*x + 1684*x^2 + 481*x^3 + 42*x^4 - 7*x^5 + x^6) / (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=4:
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..2....3....3....2....3....2....3....4....1....4....4....4....1....4....3....3
%e ..3....5....0....2....2....0....6....0....1....4....8....8....1....6....5....2
%e ..4....4....1....5....5....2....8....2....1....5....5....4....0....9....7....3
%e ..4....5....3....7....6....3....6....6....4....2....3....2....1....6...10....1
%e ..7....4....6....7....6....2....2....3....3....0....6....1....3....2....6....2
%e ..4....2....4....4....3....0....2....4....2....1....4....0....4....1....3....1
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%Y Cf. A204213.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 12 2012
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