A223834 Number of n X 4 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

11, 46, 118, 249, 471, 824, 1356, 2123, 3189, 4626, 6514, 8941, 12003, 15804, 20456, 26079, 32801, 40758, 50094, 60961, 73519, 87936, 104388, 123059, 144141, 167834, 194346, 223893, 256699, 292996, 333024, 377031, 425273, 478014, 535526, 598089

Offset

1,1

Comments

Column 4 of A223838.

Links

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

Formula

Empirical: a(n) = (1/3)*n^4 + (2/3)*n^3 + (31/6)*n^2 + (71/6)*n - 9 for n>1.

Conjectures from Colin Barker, Aug 23 2018: (Start)

G.f.: x*(11 - 9*x - 2*x^2 + 9*x^3 + x^4 - 2*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..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..1..1..0
..0..0..0..0....0..0..0..0....0..1..0..0....1..1..1..0....1..1..1..0
..0..1..1..0....0..1..1..1....0..1..1..0....1..1..1..0....1..1..1..0

Crossrefs

Cf. A223838.

Sequence in context: A282095 A063158 A081587 * A359096 A143059 A224142

Adjacent sequences: A223831 A223832 A223833 * A223835 A223836 A223837

Keyword

nonn

Author

R. H. Hardin, Mar 27 2013

Status

approved