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

1,1

Comments

Column 3 of A223620.

Links

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

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)

Example

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

Crossrefs

Cf. A223620.

Sequence in context: A181479 A223842 A212693 * A188768 A188757 A223947

Adjacent sequences: A223612 A223613 A223614 * A223616 A223617 A223618

Keyword

nonn

Author

R. H. Hardin, Mar 24 2013

Status

approved