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A229013 Number of arrays of median of three adjacent elements of some length-5 0..n array, with no adjacent equal elements in the latter. 1

%I

%S 2,15,46,101,186,307,470,681,946,1271,1662,2125,2666,3291,4006,4817,

%T 5730,6751,7886,9141,10522,12035,13686,15481,17426,19527,21790,24221,

%U 26826,29611,32582,35745,39106,42671,46446,50437,54650,59091,63766,68681,73842

%N Number of arrays of median of three adjacent elements of some length-5 0..n array, with no adjacent equal elements in the latter.

%H R. H. Hardin, <a href="/A229013/b229013.txt">Table of n, a(n) for n = 1..210</a>

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

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

%F G.f.: x*(2 - x)*(1 + 4*x + x^2) / (1 - x)^4.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

%F (End)

%e Some solutions for n=4:

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

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

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

%Y Row 3 of A229012.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 10 2013

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Last modified September 17 19:58 EDT 2021. Contains 347489 sequences. (Running on oeis4.)