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A250142 Number of length 3+2 0..n arrays with the medians of every three consecutive terms nondecreasing. 1

%I

%S 24,162,632,1827,4368,9156,17424,30789,51304,81510,124488,183911,

%T 264096,370056,507552,683145,904248,1179178,1517208,1928619,2424752,

%U 3018060,3722160,4551885,5523336,6653934,7962472,9469167,11195712,13165328

%N Number of length 3+2 0..n arrays with the medians of every three consecutive terms nondecreasing.

%H R. H. Hardin, <a href="/A250142/b250142.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (13/30)*n^5 + 3*n^4 + (22/3)*n^3 + 8*n^2 + (127/30)*n + 1.

%F Conjectures from _Colin Barker_, Nov 11 2018: (Start)

%F G.f.: x*(24 + 18*x + 20*x^2 - 15*x^3 + 6*x^4 - x^5) / (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=6:

%e ..0....5....2....2....6....3....6....0....6....2....1....3....0....5....3....4

%e ..0....3....1....2....2....1....0....5....1....2....3....3....1....1....1....3

%e ..0....0....1....3....4....4....2....4....1....6....3....4....3....5....6....3

%e ..4....6....4....4....6....4....3....6....0....0....6....5....5....6....6....0

%e ..5....3....1....5....6....2....1....6....2....2....2....6....6....1....3....5

%Y Row 3 of A250140.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 13 2014

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Last modified December 5 16:13 EST 2021. Contains 349557 sequences. (Running on oeis4.)