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

Author

R. H. Hardin, Mar 27 2013

Keywords

• nonn

Comments

Column 3 of A223770.

Examples

			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
		

Links

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

Crossrefs

Cf. A223770.

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)