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A278325 T(n,k)=Number of nXk 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.

%I A278325 #4 Nov 18 2016 06:45:00
%S A278325 0,0,0,0,3,0,1,20,20,1,6,94,236,94,6,21,395,1678,1678,395,21,56,1492,
%T A278325 9714,19854,9714,1492,56,126,4991,51229,186987,186987,51229,4991,126,
%U A278325 252,14848,251892,1548002,3058990,1548002,251892,14848,252,462,39832,1144205
%N A278325 T(n,k)=Number of nXk 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.
%C A278325 Table starts
%C A278325 ...0.....0........0..........1............6..............21................56
%C A278325 ...0.....3.......20.........94..........395............1492..............4991
%C A278325 ...0....20......236.......1678.........9714...........51229............251892
%C A278325 ...1....94.....1678......19854.......186987.........1548002..........11947350
%C A278325 ...6...395.....9714.....186987......3058990........43798840.........570738085
%C A278325 ..21..1492....51229....1548002.....43798840......1133034160.......26606146271
%C A278325 ..56..4991...251892...11947350....570738085.....26606146271.....1159826452573
%C A278325 .126.14848..1144205...87562135...7010453565....577253086055....46588303100299
%C A278325 .252.39832..4762445..605431820..82490704797..11856994168275..1741053359883624
%C A278325 .462.97835.18164685.3905165468.927749763030.234252250004719.61687083048618477
%H A278325 R. H. Hardin, <a href="/A278325/b278325.txt">Table of n, a(n) for n = 1..199</a>
%F A278325 Empirical for column k:
%F A278325 k=1: a(n) = (1/120)*n^5 - (1/24)*n^4 + (1/24)*n^3 + (1/24)*n^2 - (1/20)*n
%F A278325 k=2: [polynomial of degree 11]
%F A278325 k=3: [polynomial of degree 23]
%F A278325 k=4: [polynomial of degree 47]
%F A278325 k=5: [polynomial of degree 95]
%e A278325 Some solutions for n=4 k=4
%e A278325 ..0..1..1..1. .1..1..1..1. .0..0..1..1. .0..1..0..1. .0..0..0..0
%e A278325 ..0..0..1..0. .0..1..0..0. .0..1..1..0. .1..0..0..0. .1..0..1..1
%e A278325 ..0..1..0..0. .1..0..0..0. .1..1..0..1. .1..0..1..0. .0..0..0..1
%e A278325 ..1..1..0..0. .1..0..0..0. .0..0..1..0. .0..0..1..1. .0..1..0..0
%Y A278325 Column 1 is A000389(n+1).
%K A278325 nonn,tabl
%O A278325 1,5
%A A278325 _R. H. Hardin_, Nov 18 2016