A223835 Number of n X 5 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

16, 86, 255, 596, 1240, 2388, 4325, 7436, 12222, 19316, 29499, 43716, 63092, 88948, 122817, 166460, 221882, 291348, 377399, 482868, 610896, 764948, 948829, 1166700, 1423094, 1722932, 2071539, 2474660, 2938476, 3469620, 4075193, 4762780, 5540466

Offset

1,1

Comments

Column 5 of A223838.

Links

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

Formula

Empirical: a(n) = (2/15)*n^5 + (1/6)*n^4 + (19/6)*n^3 + (28/3)*n^2 + (126/5)*n - 36 for n>2.

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

G.f.: x*(16 - 10*x - 21*x^2 + 36*x^3 + 9*x^4 - 18*x^5 + 2*x^6 + 2*x^7) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>8.

(End)

Example

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

Crossrefs

Cf. A223838.

Sequence in context: A223962 A252834 A050256 * A224143 A225007 A352953

Adjacent sequences: A223832 A223833 A223834 * A223836 A223837 A223838

Keyword

nonn

Author

R. H. Hardin, Mar 27 2013

Status

approved