A223962 Number of 2 X n 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

16, 85, 295, 805, 1876, 3906, 7470, 13365, 22660, 36751, 57421, 86905, 127960, 183940, 258876, 357561, 485640, 649705, 857395, 1117501, 1440076, 1836550, 2319850, 2904525, 3606876, 4445091, 5439385, 6612145, 7988080, 9594376

Offset

1,1

Comments

Row 2 of A223961.

Links

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

Formula

Empirical: a(n) = (1/144)*n^6 + (7/48)*n^5 + (157/144)*n^4 + (59/16)*n^3 + (425/72)*n^2 + (25/6)*n + 1.

Conjectures from Colin Barker, Aug 24 2018: (Start)

G.f.: x*(16 - 27*x + 36*x^2 - 35*x^3 + 21*x^4 - 7*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=3:
..0..0..1....1..2..3....0..0..3....3..3..3....0..0..1....1..1..2....0..0..3
..0..0..3....2..2..3....3..3..3....3..3..3....0..2..3....1..2..3....0..3..3

Crossrefs

Cf. A223961.

Sequence in context: A172213 A231941 A118675 * A252834 A183777 A050256

Adjacent sequences: A223959 A223960 A223961 * A223963 A223964 A223965

Keyword

nonn

Author

R. H. Hardin, Mar 29 2013

Status

approved