A224410 Number of 3 X n 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

8, 36, 100, 228, 465, 879, 1568, 2668, 4362, 6890, 10560, 15760, 22971, 32781, 45900, 63176, 85612, 114384, 150860, 196620, 253477, 323499, 409032, 512724, 637550, 786838, 964296, 1174040, 1420623, 1709065, 2044884, 2434128, 2883408, 3399932

Offset

1,1

Comments

Row 3 of A224409.

Links

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

Formula

Empirical: a(n) = (1/720)*n^6 + (1/48)*n^5 + (29/144)*n^4 + (13/16)*n^3 + (2087/360)*n^2 + (7/6)*n.

Conjectures from Colin Barker, Aug 30 2018: (Start)

G.f.: x*(8 - 20*x + 16*x^2 + 4*x^3 - 11*x^4 + 4*x^5) / (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....1..0..0....1..0..0....1..1..0....1..1..0....1..1..0....0..1..1
..1..1..0....0..1..0....1..1..0....1..0..0....1..0..0....1..1..0....1..1..1
..1..0..0....1..0..0....1..1..1....0..0..0....1..1..0....1..1..0....1..1..0

Crossrefs

Cf. A224409.

Sequence in context: A035006 A245360 A032768 * A006636 A325656 A357716

Adjacent sequences: A224407 A224408 A224409 * A224411 A224412 A224413

Keyword

nonn

Author

R. H. Hardin, Apr 05 2013

Status

approved