A225012 - OEIS

%I #10 May 19 2014 07:47:12

%S 6,36,161,581,1792,4900,12174,27966,60172,122464,237590,442118,793092,

%T 1377174,2322967,3817351,6126818,9624964,14827487,22436251,33394208,

%U 48953224,70757132,100942636,142261016,198223936,273277036,373005396

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

%C Row 5 of A225010.

%C Apparently column 6 of A071920. - _R. J. Mathar_, May 17 2014

%H R. H. Hardin, <a href="/A225012/b225012.txt">Table of n, a(n) for n = 1..210</a>

%F 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.

%F 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

%e Some solutions for n=3

%e ..0..0..0....0..1..0....0..1..0....1..0..0....0..0..0....0..0..0....0..0..0

%e ..1..0..0....0..1..0....1..1..0....1..1..0....0..0..1....0..0..0....0..1..1

%e ..1..0..0....0..1..0....1..1..1....1..1..0....0..1..1....0..1..0....0..1..1

%e ..1..1..0....0..1..1....1..1..1....1..1..1....0..1..1....0..1..1....1..1..1

%e ..1..1..0....0..1..1....1..1..1....1..1..1....0..1..1....1..1..1....1..1..1

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 23 2013