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.

2, 15, 46, 101, 186, 307, 470, 681, 946, 1271, 1662, 2125, 2666, 3291, 4006, 4817, 5730, 6751, 7886, 9141, 10522, 12035, 13686, 15481, 17426, 19527, 21790, 24221, 26826, 29611, 32582, 35745, 39106, 42671, 46446, 50437, 54650, 59091, 63766, 68681, 73842

Offset

1,1

Links

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

Formula

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

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

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

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

(End)

Example

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

Crossrefs

Row 3 of A229012.

Sequence in context: A346546 A327941 A162256 * A323685 A336209 A256328

Adjacent sequences: A229010 A229011 A229012 * A229014 A229015 A229016

Keyword

nonn

Author

R. H. Hardin, Sep 10 2013

Status

approved