A224142 Number of n X 4 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

11, 46, 124, 272, 526, 930, 1536, 2404, 3602, 5206, 7300, 9976, 13334, 17482, 22536, 28620, 35866, 44414, 54412, 66016, 79390, 94706, 112144, 131892, 154146, 179110, 206996, 238024, 272422, 310426, 352280, 398236, 448554, 503502, 563356, 628400

Offset

1,1

Comments

Column 4 of A224146.

Links

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

Formula

Empirical: a(n) = (1/3)*n^4 + (4/3)*n^3 + (14/3)*n^2 + (23/3)*n - 4 for n>1.

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

G.f.: x*(11 - 9*x + 4*x^2 + 2*x^3 + x^4 - x^5) / (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>6.

(End)

Example

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

Crossrefs

Cf. A224146.

Sequence in context: A223834 A359096 A143059 * A155014 A006324 A372663

Adjacent sequences: A224139 A224140 A224141 * A224143 A224144 A224145

Keyword

nonn

Author

R. H. Hardin, Mar 31 2013

Status

approved