A224135 Number of 4 X n 0..1 arrays with rows nondecreasing and antidiagonals unimodal.

16, 81, 208, 419, 760, 1279, 2032, 3083, 4504, 6375, 8784, 11827, 15608, 20239, 25840, 32539, 40472, 49783, 60624, 73155, 87544, 103967, 122608, 143659, 167320, 193799, 223312, 256083, 292344, 332335, 376304, 424507, 477208, 534679, 597200, 665059

Offset

1,1

Comments

Row 4 of A224133.

Links

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

Formula

Empirical: a(n) = (1/3)*n^4 + 2*n^3 + (26/3)*n^2 + 18*n - 5 for n>2.

Conjectures from Colin Barker, Aug 27 2018: (Start)

G.f.: x*(16 + x - 37*x^2 + 29*x^3 + 15*x^4 - 22*x^5 + 6*x^6) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>7.

(End)

Example

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

Crossrefs

Cf. A224133.

Sequence in context: A041490 A096020 A016898 * A265154 A268198 A212898

Adjacent sequences: A224132 A224133 A224134 * A224136 A224137 A224138

Keyword

nonn

Author

R. H. Hardin, Mar 31 2013

Status

approved