A224001 Number of 3 X n 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

27, 157, 476, 1144, 2403, 4614, 8291, 14141, 23109, 36428, 55674, 82826, 120331, 171174, 238953, 327959, 443261, 590796, 777464, 1011228, 1301219, 1657846, 2092911, 2619729, 3253253, 4010204, 4909206, 5970926, 7218219, 8676278

Offset

1,1

Comments

Row 3 of A223999.

Links

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

Formula

Empirical: a(n) = (1/144)*n^6 + (5/48)*n^5 + (163/144)*n^4 + (85/16)*n^3 + (895/36)*n^2 - (65/12)*n + 3 for n>2.

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

G.f.: x*(27 - 32*x - 56*x^2 + 164*x^3 - 159*x^4 + 85*x^5 - 32*x^6 + 9*x^7 - x^8) / (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>9.

(End)

Example

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

Crossrefs

Cf. A223999.

Sequence in context: A129028 A133548 A033262 * A042418 A042420 A372560

Adjacent sequences: A223998 A223999 A224000 * A224002 A224003 A224004

Keyword

nonn

Author

R. H. Hardin, Mar 30 2013

Status

approved