A223859 Number of n X 3 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

50, 684, 4884, 24199, 93731, 303560, 857696, 2175884, 5058530, 10940664, 22267210, 43028893, 79505879, 141274716, 242543322, 403888650, 654482250, 1034900244, 1600626232, 2426368355, 3611325155, 5285548992, 7617570604, 10823463928

Offset: 1

Author

R. H. Hardin, Mar 28 2013

Keywords

• nonn

Comments

Column 3 of A223864.

Examples

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

Links

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

Crossrefs

Cf. A223864.

Formula

Empirical: a(n) = (353/181440)*n^9 + (353/10080)*n^8 + (9707/30240)*n^7 + (13/8)*n^6 + (45713/8640)*n^5 + (1809/160)*n^4 + (332021/22680)*n^3 + (6569/504)*n^2 + (7241/1260)*n - 2.

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

G.f.: x*(50 + 184*x + 294*x^2 + 139*x^3 - 59*x^4 + 165*x^5 - 117*x^6 + 66*x^7 - 18*x^8 + 2*x^9) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

(End)