A223615 Number of n X 3 0..1 arrays with rows and columns unimodal.

7, 49, 240, 876, 2582, 6504, 14547, 29659, 56161, 100123, 169786, 276030, 432888, 658106, 973749, 1406853, 1990123, 2762677, 3770836, 5068960, 6720330, 8798076, 11386151, 14580351, 18489381, 23235967, 28958014, 35809810, 43963276, 53609262

Offset: 1

Author

R. H. Hardin, Mar 24 2013

Keywords

• nonn

Comments

Column 3 of A223620.

Examples

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

Links

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

Crossrefs

Cf. A223620.

Formula

Empirical: a(n) = (23/360)*n^6 + (31/120)*n^5 + (8/9)*n^4 + (31/24)*n^3 + (737/360)*n^2 + (29/20)*n + 1.

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

G.f.: x*(7 + 44*x^2 - 20*x^3 + 20*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)