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

1,1

Comments

Column 3 of A223864.

Links

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

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)

Example

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

Crossrefs

Cf. A223864.

Sequence in context: A323485 A052460 A224168 * A223982 A128799 A231835

Adjacent sequences: A223856 A223857 A223858 * A223860 A223861 A223862

Keyword

nonn

Author

R. H. Hardin, Mar 28 2013

Status

approved