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A250142
Number of length 3+2 0..n arrays with the medians of every three consecutive terms nondecreasing.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 13 2014
STATUS
approved