A223632 Number of n X 3 0..1 arrays with rows, antidiagonals and columns unimodal.

7, 49, 229, 801, 2297, 5699, 12657, 25753, 48811, 87253, 148501, 242425, 381837, 583031, 866369, 1256913, 1785103, 2487481, 3407461, 4596145, 6113185, 8027691, 10419185, 13378601, 17009331, 21428317, 26767189, 33173449, 40811701, 49864927

Offset: 1

Author

R. H. Hardin, Mar 24 2013

Keywords

• nonn

Comments

Column 3 of A223637.

Examples

			Some solutions for n=4:
..0..0..1....1..1..0....0..0..0....1..1..0....0..1..0....0..1..0....1..1..0
..1..0..0....0..1..1....0..0..0....1..1..0....1..1..0....0..1..1....0..1..0
..0..1..0....0..1..0....1..0..0....1..1..0....0..0..1....1..1..1....0..0..0
..0..1..0....0..1..0....1..1..1....1..1..0....0..0..1....1..1..0....0..0..0
		

Links

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

Crossrefs

Cf. A223637.

Formula

Empirical: a(n) = (23/360)*n^6 + (11/120)*n^5 + (91/72)*n^4 + (11/8)*n^3 + (301/180)*n^2 + (23/15)*n + 1.

Conjectures from Colin Barker, Aug 21 2018: (Start)

G.f.: x*(7 + 33*x^2 - 18*x^3 + 29*x^4 - 6*x^5 + 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)