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A229015 Number of arrays of median of three adjacent elements of some length 7 0..n array, with no adjacent equal elements in the latter.

%I A229015 #12 Sep 13 2018 12:06:45
%S A229015 2,57,332,1145,3002,6635,13040,23515,39698,63605,97668,144773,208298,
%T A229015 292151,400808,539351,713506,929681,1195004,1517361,1905434,2368739,
%U A229015 2917664,3563507,4318514,5195917,6209972,7375997,8710410,10230767
%N A229015 Number of arrays of median of three adjacent elements of some length 7 0..n array, with no adjacent equal elements in the latter.
%H A229015 R. H. Hardin, <a href="/A229015/b229015.txt">Table of n, a(n) for n = 1..210</a>
%F A229015 Empirical: a(n) = (19/60)*n^5 + (37/12)*n^4 + (19/12)*n^3 - (61/12)*n^2 + (31/10)*n - 1.
%F A229015 Conjectures from _Colin Barker_, Sep 13 2018: (Start)
%F A229015 G.f.: x*(2 + 45*x + 20*x^2 - 32*x^3 + 2*x^4 + x^5) / (1 - x)^6.
%F A229015 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 A229015 (End)
%e A229015 Some solutions for n=4:
%e A229015 ..3....2....2....3....4....0....3....2....2....3....1....2....0....2....2....0
%e A229015 ..2....1....2....1....0....4....3....3....3....2....1....2....2....2....0....2
%e A229015 ..4....2....1....3....4....0....1....0....0....2....3....0....3....4....2....3
%e A229015 ..1....3....4....1....1....3....1....3....3....1....0....3....3....0....0....4
%e A229015 ..4....4....2....1....4....0....3....0....3....4....3....3....4....1....4....3
%Y A229015 Row 5 of A229012.
%K A229015 nonn
%O A229015 1,1
%A A229015 _R. H. Hardin_, Sep 10 2013