A223639 Number of n X 3 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.

7, 49, 218, 726, 2014, 4904, 10797, 21917, 41601, 74635, 127636, 209480, 331776, 509386, 760991, 1109703, 1583723, 2217045, 3050206, 4131082, 5515730, 7269276, 9466849, 12194561, 15550533, 19645967, 24606264, 30572188, 37701076, 46168094

Offset: 1

Author

R. H. Hardin, Mar 24 2013

Keywords

• nonn

Comments

Column 3 of A223644.

Examples

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

Links

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

Crossrefs

Cf. A223644.

Formula

Empirical: a(n) = (23/360)*n^6 - (3/40)*n^5 + (31/18)*n^4 + (5/8)*n^3 + (1517/360)*n^2 - (51/20)*n + 3.

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

G.f.: x*(7 + 22*x^2 - 16*x^3 + 40*x^4 - 10*x^5 + 3*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)