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A223765 Number of n X 3 0..1 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing. 1
7, 28, 71, 155, 317, 607, 1097, 1887, 3112, 4950, 7631, 11447, 16763, 24029, 33793, 46715, 63582, 85324, 113031, 147971, 191609, 245627, 311945, 392743, 490484, 607938, 748207, 914751, 1111415, 1342457, 1612577, 1926947, 2291242, 2711672 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 3 of A223770.

LINKS

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

FORMULA

Empirical: a(n) = (1/720)*n^6 + (1/240)*n^5 + (41/144)*n^4 - (13/48)*n^3 + (2237/360)*n^2 - (217/30)*n + 19 for n>2.

Conjectures from Colin Barker, Aug 22 2018: (Start)

G.f.: x*(7 - 21*x + 22*x^2 + x^3 - 12*x^4 - 9*x^5 + 26*x^6 - 17*x^7 + 4*x^8) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>9.

(End)

EXAMPLE

Some solutions for n=3:

..0..0..0....0..0..0....0..0..0....0..0..0....0..0..1....1..1..0....1..1..0

..0..0..0....1..0..0....0..0..1....0..1..1....0..1..1....0..1..1....1..1..1

..1..0..0....1..1..1....1..1..0....0..0..1....1..1..1....0..1..1....1..1..1

CROSSREFS

Cf. A223770.

Sequence in context: A176362 A008457 A138503 * A064951 A296986 A211899

Adjacent sequences:  A223762 A223763 A223764 * A223766 A223767 A223768

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 27 2013

STATUS

approved

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Last modified April 5 00:43 EDT 2020. Contains 333238 sequences. (Running on oeis4.)