A223764 Number of n X 2 0..1 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.

4, 12, 28, 56, 101, 169, 267, 403, 586, 826, 1134, 1522, 2003, 2591, 3301, 4149, 5152, 6328, 7696, 9276, 11089, 13157, 15503, 18151, 21126, 24454, 28162, 32278, 36831, 41851, 47369, 53417, 60028, 67236, 75076, 83584, 92797, 102753, 113491, 125051

Offset

1,1

Comments

Column 2 of A223770.

Links

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

Formula

Empirical: a(n) = (1/24)*n^4 + (1/4)*n^3 + (35/24)*n^2 + (5/4)*n + 1.

Conjectures from Colin Barker, Feb 21 2018: (Start)

G.f.: x*(2 - 2*x + x^2)^2 / (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....0..0....0..0....1..0....1..1....0..0....0..1....0..1....0..0....0..1
..0..0....0..0....1..1....0..1....0..1....1..0....1..1....0..0....1..0....0..1
..1..1....0..1....1..1....0..0....0..1....0..1....0..1....0..0....1..1....1..0

Crossrefs

Cf. A223770.

Sequence in context: A161216 A085622 A011940 * A102653 A102650 A011939

Adjacent sequences: A223761 A223762 A223763 * A223765 A223766 A223767

Keyword

nonn

Author

R. H. Hardin, Mar 27 2013

Status

approved