A224147 Number of 3 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

4, 16, 49, 124, 275, 554, 1037, 1831, 3082, 4984, 7789, 11818, 17473, 25250, 35753, 49709, 67984, 91600, 121753, 159832, 207439, 266410, 338837, 427091, 533846, 662104, 815221, 996934, 1211389, 1463170, 1757329, 2099417, 2495516, 2952272

Offset

1,1

Comments

Row 3 of A224146.

Links

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

Formula

Empirical: a(n) = (1/720)*n^6 + (1/80)*n^5 + (23/144)*n^4 + (29/48)*n^3 + (241/180)*n^2 + (53/60)*n + 1.

Conjectures from Colin Barker, Aug 28 2018: (Start)

G.f.: x*(4 - 12*x + 21*x^2 - 23*x^3 + 16*x^4 - 6*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..0....0..0..0....0..0..1....0..1..0....0..0..0....0..0..0....0..0..0
..0..1..1....0..0..0....0..0..1....0..1..0....0..0..1....1..0..0....1..1..1
..1..1..1....0..0..0....0..1..1....0..1..0....0..0..1....1..1..0....1..1..1

Crossrefs

Cf. A224146.

Sequence in context: A119005 A237986 A086601 * A227266 A114185 A188516

Adjacent sequences: A224144 A224145 A224146 * A224148 A224149 A224150

Keyword

nonn

Author

R. H. Hardin, Mar 31 2013

Status

approved