A229017 Number of arrays of median of three adjacent elements of some length 9 0..n array, with no adjacent equal elements in the latter.

2, 193, 2054, 10735, 38768, 111311, 273124, 597477, 1197190, 2238005, 3954490, 6668675, 10811620, 16948115, 25804712, 38301289, 55586346, 79076233, 110498510, 151939639, 205897208, 275336887, 363754316, 475242125, 614562286, 787223997

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..158

Formula

Empirical: a(n) = (5/126)*n^7 + (233/180)*n^6 + (1073/180)*n^5 - (85/18)*n^4 - (89/36)*n^3 + (617/180)*n^2 - (177/70)*n + 1.

Conjectures from Colin Barker, Sep 14 2018: (Start)

G.f.: x*(2 + 177*x + 566*x^2 - 405*x^3 - 268*x^4 + 121*x^5 + 8*x^6 - x^7) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

Example

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

Crossrefs

Row 7 of A229012.

Sequence in context: A260404 A064682 A139949 * A103429 A316901 A316888

Adjacent sequences: A229014 A229015 A229016 * A229018 A229019 A229020

Keyword

nonn

Author

R. H. Hardin, Sep 10 2013

Status

approved