A250142 Number of length 3+2 0..n arrays with the medians of every three consecutive terms nondecreasing.

24, 162, 632, 1827, 4368, 9156, 17424, 30789, 51304, 81510, 124488, 183911, 264096, 370056, 507552, 683145, 904248, 1179178, 1517208, 1928619, 2424752, 3018060, 3722160, 4551885, 5523336, 6653934, 7962472, 9469167, 11195712, 13165328

Offset

1,1

Links

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

Formula

Empirical: a(n) = (13/30)*n^5 + 3*n^4 + (22/3)*n^3 + 8*n^2 + (127/30)*n + 1.

Conjectures from Colin Barker, Nov 11 2018: (Start)

G.f.: x*(24 + 18*x + 20*x^2 - 15*x^3 + 6*x^4 - x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

Some solutions for n=6:
..0....5....2....2....6....3....6....0....6....2....1....3....0....5....3....4
..0....3....1....2....2....1....0....5....1....2....3....3....1....1....1....3
..0....0....1....3....4....4....2....4....1....6....3....4....3....5....6....3
..4....6....4....4....6....4....3....6....0....0....6....5....5....6....6....0
..5....3....1....5....6....2....1....6....2....2....2....6....6....1....3....5

Crossrefs

Row 3 of A250140.

Sequence in context: A294110 A136380 A250323 * A019583 A244908 A087887

Adjacent sequences: A250139 A250140 A250141 * A250143 A250144 A250145

Keyword

nonn

Author

R. H. Hardin, Nov 13 2014

Status

approved