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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 21 10:32 EDT 2021. Contains 348150 sequences. (Running on oeis4.)