A224039 Number of 3 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

8, 21, 37, 58, 85, 119, 161, 212, 273, 345, 429, 526, 637, 763, 905, 1064, 1241, 1437, 1653, 1890, 2149, 2431, 2737, 3068, 3425, 3809, 4221, 4662, 5133, 5635, 6169, 6736, 7337, 7973, 8645, 9354, 10101, 10887, 11713, 12580, 13489, 14441, 15437, 16478

Offset

1,1

Comments

Row 3 of A224038.

Links

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

Formula

Empirical: a(n) = (1/6)*n^3 + 1*n^2 + (47/6)*n for n>1.

Conjectures from Colin Barker, Aug 26 2018: (Start)

G.f.: x*(8 - 11*x + x^2 + 4*x^3 - x^4) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.

(End)

Example

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

Crossrefs

Cf. A224038.

Sequence in context: A154894 A241986 A179681 * A279895 A225287 A000567

Adjacent sequences: A224036 A224037 A224038 * A224040 A224041 A224042

Keyword

nonn

Author

R. H. Hardin, Mar 30 2013

Status

approved