A225012 Number of 5 X n 0..1 arrays with rows unimodal and columns nondecreasing.

6, 36, 161, 581, 1792, 4900, 12174, 27966, 60172, 122464, 237590, 442118, 793092, 1377174, 2322967, 3817351, 6126818, 9624964, 14827487, 22436251, 33394208, 48953224, 70757132, 100942636, 142261016, 198223936, 273277036, 373005396

Offset

1,1

Comments

Row 5 of A225010.

Apparently column 6 of A071920. - R. J. Mathar, May 17 2014

Links

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

Formula

Empirical: a(n) = (1/3628800)*n^10 + (1/80640)*n^9 + (1/3780)*n^8 + (19/5760)*n^7 + (4633/172800)*n^6 + (331/2304)*n^5 + (191249/362880)*n^4 + (24421/20160)*n^3 + (10897/5600)*n^2 + (137/120)*n + 1 = 1 + n*(n+1)* (n^8 + 44*n^7 + 916*n^6 + 11054*n^5 + 86239*n^4 + 435086*n^3 + 1477404*n^2 + 2918376*n + 4142880)/ 3628800.

Empirical: G.f.: -x*(x^2 - 3*x + 3) *(x^2 - 2*x + 2) *(x^2 - x + 1) *(x^4 - 4*x^3 + 5*x^2 - 2*x + 1) / (x-1)^11. - R. J. Mathar, May 17 2014

Example

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

Crossrefs

Sequence in context: A225380 A371157 A371197 * A228458 A203050 A203332

Adjacent sequences: A225009 A225010 A225011 * A225013 A225014 A225015

Keyword

nonn

Author

R. H. Hardin, Apr 23 2013

Status

approved