A223913 Number of n X 3 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.

22, 158, 666, 2111, 5548, 12752, 26494, 50863, 91634, 156682, 256442, 404415, 617720, 917692, 1330526, 1887967, 2628046, 3595862, 4844410, 6435455, 8440452, 10941512, 14032414, 17819663, 22423594, 27979522, 34638938, 42570751, 51962576

Offset: 1

Author

R. H. Hardin, Mar 29 2013

Keywords

• nonn

Comments

Column 3 of A223918.

Examples

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

Links

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

Crossrefs

Cf. A223918.

Formula

Empirical: a(n) = (23/360)*n^6 + (23/40)*n^5 + (205/72)*n^4 + (143/24)*n^3 + (364/45)*n^2 + (82/15)*n - 1.

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

G.f.: x*(22 + 4*x + 22*x^2 - 3*x^3 - 3*x^4 + 5*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)