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

1,2

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A000574(n+1).

Sequence in context: A209055 A209212 A222847 * A048234 A068415 A127539

Adjacent sequences: A278306 A278307 A278308 * A278310 A278311 A278312

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 17 2016

Status

approved