A223950 Number of 3 X n 0..1 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

8, 27, 54, 96, 157, 241, 352, 494, 671, 887, 1146, 1452, 1809, 2221, 2692, 3226, 3827, 4499, 5246, 6072, 6981, 7977, 9064, 10246, 11527, 12911, 14402, 16004, 17721, 19557, 21516, 23602, 25819, 28171, 30662, 33296, 36077, 39009, 42096, 45342, 48751, 52327

Offset

1,1

Comments

Row 3 of A223949.

Links

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

Formula

Empirical: a(n) = (2/3)*n^3 + (3/2)*n^2 + (41/6)*n + 2 for n>1.

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

G.f.: x*(8 - 5*x - 6*x^2 + 10*x^3 - 3*x^4) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.

(End)

Example

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

Crossrefs

Cf. A223949.

Sequence in context: A122013 A250230 A250278 * A339897 A131620 A141227

Adjacent sequences: A223947 A223948 A223949 * A223951 A223952 A223953

Keyword

nonn

Author

R. H. Hardin, Mar 29 2013

Status

approved