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A223859 Number of n X 3 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing. 1
50, 684, 4884, 24199, 93731, 303560, 857696, 2175884, 5058530, 10940664, 22267210, 43028893, 79505879, 141274716, 242543322, 403888650, 654482250, 1034900244, 1600626232, 2426368355, 3611325155, 5285548992, 7617570604, 10823463928 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 3 of A223864.

LINKS

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

FORMULA

Empirical: a(n) = (353/181440)*n^9 + (353/10080)*n^8 + (9707/30240)*n^7 + (13/8)*n^6 + (45713/8640)*n^5 + (1809/160)*n^4 + (332021/22680)*n^3 + (6569/504)*n^2 + (7241/1260)*n - 2.

Conjectures from Colin Barker, Aug 24 2018: (Start)

G.f.: x*(50 + 184*x + 294*x^2 + 139*x^3 - 59*x^4 + 165*x^5 - 117*x^6 + 66*x^7 - 18*x^8 + 2*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:

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

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

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

CROSSREFS

Cf. A223864.

Sequence in context: A323485 A052460 A224168 * A223982 A128799 A231835

Adjacent sequences:  A223856 A223857 A223858 * A223860 A223861 A223862

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 28 2013

STATUS

approved

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Last modified February 22 18:03 EST 2020. Contains 332148 sequences. (Running on oeis4.)