A229016 Number of arrays of median of three adjacent elements of some length 8 0..n array, with no adjacent equal elements in the latter.

2, 105, 830, 3527, 10860, 27379, 60180, 119653, 220318, 381749, 629586, 996635, 1524056, 2262639, 3274168, 4632873, 6426970, 8760289, 11753990, 15548367, 20304740, 26207435, 33465852, 42316621, 53025846, 65891437, 81245530, 99456995

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..178

Formula

Empirical: a(n) = (11/90)*n^6 + (11/5)*n^5 + (167/36)*n^4 - (43/6)*n^3 + (583/180)*n^2 - (61/30)*n + 1.

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

G.f.: x*(2 + 91*x + 137*x^2 - 148*x^3 - 4*x^4 + 9*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

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

Crossrefs

Row 6 of A229012.

Sequence in context: A258828 A156880 A280095 * A222840 A356723 A260579

Adjacent sequences: A229013 A229014 A229015 * A229017 A229018 A229019

Keyword

nonn

Author

R. H. Hardin, Sep 10 2013

Status

approved