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
Keywords
Examples
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
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
Comments