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A224168 Number of n X 3 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing. 1
50, 684, 4739, 22988, 87878, 282372, 794220, 2010035, 4668304, 10095924, 20559019, 39765666, 73565736, 130901340, 225070360, 375375241, 609239622, 964886492, 1494683371, 2269272536, 3382617538, 4958111188, 7155904828, 10181634047 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 3 of A224173.

LINKS

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

FORMULA

Empirical: a(n) = (353/181440)*n^9 + (17/560)*n^8 + (9083/30240)*n^7 + (1039/720)*n^6 + (46769/8640)*n^5 + (3863/360)*n^4 + (411149/22680)*n^3 + (14863/1260)*n^2 + (6497/1260)*n - 3.

Conjectures from Colin Barker, Aug 28 2018: (Start)

G.f.: x*(50 + 184*x + 149*x^2 + 378*x^3 - 327*x^4 + 412*x^5 - 228*x^6 + 107*x^7 - 22*x^8 + 3*x^9) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

(End)

EXAMPLE

Some solutions for n=3:

..0..0..1....1..1..0....2..2..2....0..0..1....0..0..1....1..0..0....2..2..1

..1..2..1....2..1..0....2..2..2....1..2..1....0..0..1....2..3..2....3..3..1

..2..2..3....2..3..3....2..2..3....3..3..1....0..2..2....3..3..3....3..3..3

CROSSREFS

Cf. A224173.

Sequence in context: A282766 A323485 A052460 * A223859 A223982 A128799

Adjacent sequences:  A224165 A224166 A224167 * A224169 A224170 A224171

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 31 2013

STATUS

approved

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Last modified February 25 02:54 EST 2020. Contains 332217 sequences. (Running on oeis4.)