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%I A205342 #8 Jun 11 2018 11:53:16
%S A205342 2,11,35,82,160,277,441,660,942,1295,1727,2246,2860,3577,4405,5352,
%T A205342 6426,7635,8987,10490,12152,13981,15985,18172,20550,23127,25911,28910,
%U A205342 32132,35585,39277,43216,47410,51867,56595,61602,66896,72485,78377,84580,91102
%N A205342 Number of length 5 nonnegative integer arrays starting and ending with 0 with adjacent elements unequal but differing by no more than n.
%C A205342 Row 4 of A205341.
%H A205342 R. H. Hardin, <a href="/A205342/b205342.txt">Table of n, a(n) for n = 1..210</a>
%F A205342 Empirical: a(n) = (4/3)*n^3 - (1/2)*n^2 + (7/6)*n.
%F A205342 Conjectures from _Colin Barker_, Jun 11 2018: (Start)
%F A205342 G.f.: x*(2 + 3*x + 3*x^2) / (1 - x)^4.
%F A205342 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F A205342 (End)
%e A205342 Some solutions for n=5:
%e A205342 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A205342 ..2....5....3....2....2....1....5....2....5....4....1....5....4....4....5....2
%e A205342 ..0....8....6....4....6....6....1....7....1....9....6....7....5....2....8....5
%e A205342 ..3....3....5....1....5....2....2....3....5....4....5....4....2....4....5....4
%e A205342 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%Y A205342 Cf. A205341.
%K A205342 nonn
%O A205342 1,1
%A A205342 _R. H. Hardin_, Jan 26 2012

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