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.

2, 57, 332, 1145, 3002, 6635, 13040, 23515, 39698, 63605, 97668, 144773, 208298, 292151, 400808, 539351, 713506, 929681, 1195004, 1517361, 1905434, 2368739, 2917664, 3563507, 4318514, 5195917, 6209972, 7375997, 8710410, 10230767

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = (19/60)*n^5 + (37/12)*n^4 + (19/12)*n^3 - (61/12)*n^2 + (31/10)*n - 1.

Conjectures from Colin Barker, Sep 13 2018: (Start)

G.f.: x*(2 + 45*x + 20*x^2 - 32*x^3 + 2*x^4 + x^5) / (1 - x)^6.

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.

(End)

Example

Some solutions for n=4:
..3....2....2....3....4....0....3....2....2....3....1....2....0....2....2....0
..2....1....2....1....0....4....3....3....3....2....1....2....2....2....0....2
..4....2....1....3....4....0....1....0....0....2....3....0....3....4....2....3
..1....3....4....1....1....3....1....3....3....1....0....3....3....0....0....4
..4....4....2....1....4....0....3....0....3....4....3....3....4....1....4....3

Crossrefs

Row 5 of A229012.

Sequence in context: A041391 A245783 A189057 * A324318 A058196 A024237

Adjacent sequences: A229012 A229013 A229014 * A229016 A229017 A229018

Keyword

nonn

Author

R. H. Hardin, Sep 10 2013

Status

approved