A223765 Number of n X 3 0..1 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.

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

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: A358999 A008457 A138503 * A064951 A296986 A211899

Adjacent sequences: A223762 A223763 A223764 * A223766 A223767 A223768

Keyword

nonn

Author

R. H. Hardin, Mar 27 2013

Status

approved