A223772 Number of n X 3 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing.

7, 28, 78, 180, 371, 707, 1269, 2170, 3563, 5650, 8692, 13020, 19047, 27281, 38339, 52962, 72031, 96584, 127834, 167188, 216267, 276927, 351281, 441722, 550947, 681982, 838208, 1023388, 1241695, 1497741, 1796607, 2143874, 2545655, 3008628

Offset: 1

Author

R. H. Hardin, Mar 27 2013

Keywords

• nonn

Comments

Column 3 of A223777.

Examples

			Some solutions for n=3:
..0..1..1....1..0..0....1..1..1....1..0..0....1..0..0....0..0..0....0..1..0
..1..1..0....1..0..0....1..1..1....1..0..0....1..0..0....0..1..0....1..1..0
..1..0..0....0..0..0....1..1..1....1..1..0....1..1..1....1..1..1....1..0..0
		

Links

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

Crossrefs

Cf. A223777.

Formula

Empirical: a(n) = (1/720)*n^6 + (1/80)*n^5 + (29/144)*n^4 + (25/48)*n^3 + (1727/360)*n^2 - (8/15)*n + 2.

Conjectures from Colin Barker, Aug 23 2018: (Start)

G.f.: x*(7 - 21*x + 29*x^2 - 23*x^3 + 14*x^4 - 7*x^5 + 2*x^6) / (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>7.

(End)