A224000 Number of 2 X n 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

9, 31, 76, 155, 281, 469, 736, 1101, 1585, 2211, 3004, 3991, 5201, 6665, 8416, 10489, 12921, 15751, 19020, 22771, 27049, 31901, 37376, 43525, 50401, 58059, 66556, 75951, 86305, 97681, 110144, 123761, 138601, 154735, 172236, 191179, 211641, 233701

Offset

1,1

Comments

Row 2 of A223999.

Links

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

Formula

Empirical: a(n) = (1/12)*n^4 + 1*n^3 + (41/12)*n^2 + (7/2)*n + 1.

Conjectures from Colin Barker, Aug 25 2018: (Start)

G.f.: x*(9 - 14*x + 11*x^2 - 5*x^3 + x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

Some solutions for n=3:
..0..0..2....0..0..1....1..1..1....0..1..1....1..1..1....0..0..2....1..1..2
..0..0..2....2..2..2....0..1..2....0..1..2....0..1..1....2..2..2....0..2..2

Crossrefs

Cf. A223999.

Sequence in context: A004126 A344675 A177342 * A118444 A321598 A048374

Adjacent sequences: A223997 A223998 A223999 * A224001 A224002 A224003

Keyword

nonn

Author

R. H. Hardin, Mar 30 2013

Status

approved