A249884 Number of length 1+6 0..n arrays with no seven consecutive terms having the maximum of any three terms equal to the minimum of the remaining four terms.

35, 805, 7420, 40740, 161315, 510965, 1377040, 3284400, 7120155, 14296205, 26954620, 48220900, 82510155, 135891245, 216513920, 335104000, 505531635, 745457685, 1077063260, 1527867460, 2131638355, 2929402245, 3970556240

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^7 + (7/2)*n^6 + 7*n^5 + (35/4)*n^4 + (49/6)*n^3 + (21/4)*n^2 + (4/3)*n.

Conjectures from Colin Barker, Nov 10 2018: (Start)

G.f.: 35*x*(1 + x)*(1 + 4*x + x^2)*(1 + 10*x + x^2) / (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=5:
..2....1....1....0....2....0....0....1....0....4....0....2....0....2....1....1
..5....2....5....1....0....5....2....3....2....0....2....3....3....0....4....1
..2....1....0....5....2....5....5....0....3....0....3....4....5....1....5....5
..5....5....0....5....1....2....2....0....0....3....3....4....2....4....1....4
..1....5....0....3....0....0....4....0....0....3....5....4....4....3....5....5
..0....3....2....1....3....3....0....3....5....2....0....0....4....5....4....1
..1....0....3....3....3....4....0....3....3....4....3....0....4....1....3....2

Crossrefs

Row 1 of A249883.

Sequence in context: A028024 A226941 A249883 * A223957 A109508 A267834

Adjacent sequences: A249881 A249882 A249883 * A249885 A249886 A249887

Keyword

nonn

Author

R. H. Hardin, Nov 07 2014

Status

approved