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

Author

R. H. Hardin, Sep 10 2013

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Row 6 of A229012.

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)