A278309 T(n,k)=Number of nXk 0..2 arrays with rows and columns in lexicographic nondecreasing order but with exactly one mistake.

0, 3, 3, 16, 32, 16, 51, 294, 294, 51, 126, 2089, 4558, 2089, 126, 266, 11486, 70795, 70795, 11486, 266, 504, 51562, 986014, 2360544, 986014, 51562, 504, 882, 197981, 11557658, 79562696, 79562696, 11557658, 197981, 882, 1452, 672365, 114457714

Offset: 1

Author

R. H. Hardin, Nov 17 2016

Keywords

• nonn
• tabl

Comments

Table starts

...0......3........16............51..............126.................266

...3.....32.......294..........2089............11486...............51562

..16....294......4558.........70795...........986014............11557658

..51...2089.....70795.......2360544.........79562696..........2506281752

.126..11486....986014......79562696.......6345491150........507575149862

.266..51562..11557658....2506281752.....507575149862.....100825279690194

.504.197981.114457714...69684770828...38819080346585...20065923383306483

.882.672365.979384739.1689884963173.2710823731820118.3886257287342627627

Examples

			Some solutions for n=3 k=4
..1..2..1..2. .0..2..2..1. .1..1..1..2. .1..2..2..2. .0..1..1..2
..2..0..0..1. .2..0..1..2. .2..2..2..0. .0..0..1..2. .0..0..2..2
..2..1..1..1. .2..1..2..2. .0..1..1..1. .0..1..2..2. .1..1..2..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..127

Crossrefs

Column 1 is A000574(n+1).

Formula

Empirical for column k:

k=1: a(n) = (1/120)*n^5 + (1/8)*n^4 + (5/24)*n^3 - (1/8)*n^2 - (13/60)*n

k=2: [polynomial of degree 17]

k=3: [polynomial of degree 53]

k=4: [polynomial of degree 161]