A224257 Number of n X 3 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.

22, 158, 648, 2017, 5246, 11990, 24842, 47643, 85838, 146878, 240668, 380061, 581398, 865094, 1256270, 1785431, 2489190, 3411038, 4602160, 6122297, 8040654, 10436854, 13401938, 17039411, 21466334, 26814462, 33231428, 40881973, 49949222

Offset

1,1

Comments

Column 3 of A224262.

Links

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

Formula

Empirical: a(n) = (23/360)*n^6 + (19/40)*n^5 + (211/72)*n^4 + (119/24)*n^3 + (2161/180)*n^2 + (77/30)*n - 1.

Conjectures from Colin Barker, Aug 29 2018: (Start)

G.f.: x*(22 + 4*x + 4*x^2 + 29*x^3 - 25*x^4 + 13*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..1..0....0..0..1....0..1..1....2..2..0....0..0..0....1..2..0....0..0..0
..2..1..0....0..1..1....2..2..2....2..2..0....2..1..1....2..2..1....0..0..0
..2..1..1....1..1..2....2..2..2....2..2..2....2..2..1....2..2..2....2..2..0

Crossrefs

Cf. A224262.

Sequence in context: A130438 A041934 A027943 * A244868 A223913 A189416

Adjacent sequences: A224254 A224255 A224256 * A224258 A224259 A224260

Keyword

nonn

Author

R. H. Hardin, Apr 02 2013

Status

approved