A278309 - OEIS

%I #4 Nov 17 2016 07:08:41

%S 0,3,3,16,32,16,51,294,294,51,126,2089,4558,2089,126,266,11486,70795,

%T 70795,11486,266,504,51562,986014,2360544,986014,51562,504,882,197981,

%U 11557658,79562696,79562696,11557658,197981,882,1452,672365,114457714

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

%C Table starts

%C ...0......3........16............51..............126.................266

%C ...3.....32.......294..........2089............11486...............51562

%C ..16....294......4558.........70795...........986014............11557658

%C ..51...2089.....70795.......2360544.........79562696..........2506281752

%C .126..11486....986014......79562696.......6345491150........507575149862

%C .266..51562..11557658....2506281752.....507575149862.....100825279690194

%C .504.197981.114457714...69684770828...38819080346585...20065923383306483

%C .882.672365.979384739.1689884963173.2710823731820118.3886257287342627627

%H R. H. Hardin, <a href="/A278309/b278309.txt">Table of n, a(n) for n = 1..127</a>

%F Empirical for column k:

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

%F k=2: [polynomial of degree 17]

%F k=3: [polynomial of degree 53]

%F k=4: [polynomial of degree 161]

%e Some solutions for n=3 k=4

%e ..1..2..1..2. .0..2..2..1. .1..1..1..2. .1..2..2..2. .0..1..1..2

%e ..2..0..0..1. .2..0..1..2. .2..2..2..0. .0..0..1..2. .0..0..2..2

%e ..2..1..1..1. .2..1..2..2. .0..1..1..1. .0..1..2..2. .1..1..2..1

%Y Column 1 is A000574(n+1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Nov 17 2016