A250061 Number of length 2+6 0..n arrays with no seven consecutive terms having the maximum of any two terms equal to the minimum of the remaining five terms.

21, 1299, 18966, 142170, 715155, 2753061, 8746524, 24049476, 59084865, 132643335, 276590226, 542336574, 1009470111, 1796982585, 3077570040, 5095523016, 8188763949, 12815629371, 19587034830, 29304700770, 43006157931, 62017291149

Offset

1,1

Comments

Row 2 of A250059.

Links

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

Formula

Empirical: a(n) = n^8 + (18/7)*n^7 + 6*n^6 + 9*n^5 + 3*n^4 - n^3 + (1/2)*n^2 - (1/14)*n.

Conjectures from Colin Barker, Aug 22 2017: (Start)

G.f.: 3*x*(7 + 370*x + 2677*x^2 + 5492*x^3 + 3977*x^4 + 890*x^5 + 27*x^6) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

(End)

Example

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

Crossrefs

Sequence in context: A036059 A036519 A219408 * A267949 A268096 A281432

Adjacent sequences: A250058 A250059 A250060 * A250062 A250063 A250064

Keyword

nonn

Author

R. H. Hardin, Nov 11 2014

Status

approved