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

%I A278309 #4 Nov 17 2016 07:08:41
%S A278309 0,3,3,16,32,16,51,294,294,51,126,2089,4558,2089,126,266,11486,70795,
%T A278309 70795,11486,266,504,51562,986014,2360544,986014,51562,504,882,197981,
%U A278309 11557658,79562696,79562696,11557658,197981,882,1452,672365,114457714
%N A278309 T(n,k)=Number of nXk 0..2 arrays with rows and columns in lexicographic nondecreasing order but with exactly one mistake.
%C A278309 Table starts
%C A278309 ...0......3........16............51..............126.................266
%C A278309 ...3.....32.......294..........2089............11486...............51562
%C A278309 ..16....294......4558.........70795...........986014............11557658
%C A278309 ..51...2089.....70795.......2360544.........79562696..........2506281752
%C A278309 .126..11486....986014......79562696.......6345491150........507575149862
%C A278309 .266..51562..11557658....2506281752.....507575149862.....100825279690194
%C A278309 .504.197981.114457714...69684770828...38819080346585...20065923383306483
%C A278309 .882.672365.979384739.1689884963173.2710823731820118.3886257287342627627
%H A278309 R. H. Hardin, <a href="/A278309/b278309.txt">Table of n, a(n) for n = 1..127</a>
%F A278309 Empirical for column k:
%F A278309 k=1: a(n) = (1/120)*n^5 + (1/8)*n^4 + (5/24)*n^3 - (1/8)*n^2 - (13/60)*n
%F A278309 k=2: [polynomial of degree 17]
%F A278309 k=3: [polynomial of degree 53]
%F A278309 k=4: [polynomial of degree 161]
%e A278309 Some solutions for n=3 k=4
%e A278309 ..1..2..1..2. .0..2..2..1. .1..1..1..2. .1..2..2..2. .0..1..1..2
%e A278309 ..2..0..0..1. .2..0..1..2. .2..2..2..0. .0..0..1..2. .0..0..2..2
%e A278309 ..2..1..1..1. .2..1..2..2. .0..1..1..1. .0..1..2..2. .1..1..2..1
%Y A278309 Column 1 is A000574(n+1).
%K A278309 nonn,tabl
%O A278309 1,2
%A A278309 _R. H. Hardin_, Nov 17 2016