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%I #8 Jun 11 2018 15:52:46
%S 5,93,689,2912,8927,22297,48335,94456,170529,289229,466389,721352,
%T 1077323,1561721,2206531,3048656,4130269,5499165,7209113,9320208,
%U 11899223,15019961,18763607,23219080,28483385,34661965,41869053,50228024
%N Number of length 7 nonnegative integer arrays starting and ending with 0 with adjacent elements unequal but differing by no more than n.
%C Row 6 of A205341.
%H R. H. Hardin, <a href="/A205344/b205344.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (44/15)*n^5 - (5/12)*n^4 + (5/12)*n^2 + (31/15)*n.
%F Conjectures from _Colin Barker_, Jun 11 2018: (Start)
%F G.f.: x*(5 + 63*x + 206*x^2 + 73*x^3 + 5*x^4) / (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>6.
%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 ..1....1....5....3....5....1....1....5....4....3....5....4....5....1....3....4
%e ..6....4...10....6....0....2....4....3....8....6...10....3....8....5....1....7
%e ..8....1....5....1....2....0....8....6....7....5....6....6....7....1....5....6
%e ..7....4....3....5....4....4....6....5....3....3....2....7....5....5....3....7
%e ..4....3....5....2....1....3....1....2....2....1....4....5....1....2....2....3
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%Y Cf. A205341.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 26 2012
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