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A229014 Number of arrays of median of three adjacent elements of some length 6 0..n array, with no adjacent equal elements in the latter. 1

%I #11 Sep 13 2018 11:11:33

%S 2,31,130,359,794,1527,2666,4335,6674,9839,14002,19351,26090,34439,

%T 44634,56927,71586,88895,109154,132679,159802,190871,226250,266319,

%U 311474,362127,418706,481655,551434,628519,713402,806591,908610,1019999,1141314

%N Number of arrays of median of three adjacent elements of some length 6 0..n array, with no adjacent equal elements in the latter.

%H R. H. Hardin, <a href="/A229014/b229014.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (2/3)*n^4 + (10/3)*n^3 - (5/3)*n^2 + (2/3)*n - 1.

%F Conjectures from _Colin Barker_, Sep 13 2018: (Start)

%F G.f.: x*(2 - x)*(1 + 11*x + 3*x^2 + x^3) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

%F (End)

%e Some solutions for n=4:

%e ..2....3....2....3....3....1....3....0....0....0....2....2....4....3....1....2

%e ..0....3....4....3....3....1....2....3....1....2....1....4....1....2....3....0

%e ..2....0....2....1....3....3....3....2....2....3....2....0....1....4....3....3

%e ..3....4....2....3....3....1....1....2....2....3....1....2....0....1....4....3

%Y Row 4 of A229012.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 10 2013

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