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A278778 T(n,k)=Number of nXk 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly two mistakes.

%I A278778 #4 Nov 28 2016 08:23:37
%S A278778 0,0,0,0,2,0,1,20,20,1,6,117,266,117,6,21,503,1972,1972,503,21,56,
%T A278778 1750,10784,19750,10784,1750,56,126,5209,48501,150085,150085,48501,
%U A278778 5209,126,252,13751,189595,955347,1673658,955347,189595,13751,252,462,33000
%N A278778 T(n,k)=Number of nXk 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly two mistakes.
%C A278778 Table starts
%C A278778 ...0.....0.......0.........1...........6............21..............56
%C A278778 ...0.....2......20.......117.........503..........1750............5209
%C A278778 ...0....20.....266......1972.......10784.........48501..........189595
%C A278778 ...1...117....1972.....19750......150085........955347.........5355983
%C A278778 ...6...503...10784....150085.....1673658......16205001.......141166787
%C A278778 ..21..1750...48501....955347....16205001.....251740932......3634987413
%C A278778 ..56..5209..189595...5355983...141166787....3634987413.....90752836672
%C A278778 .126.13751..665212..27218249..1126917480...48847405083...2155380363189
%C A278778 .252.33000.2138149.127644118..8340736743..611199661843..48042054699217
%C A278778 .462.73282.6384894.559023840.57745890265.7140933364136.999491681597761
%H A278778 R. H. Hardin, <a href="/A278778/b278778.txt">Table of n, a(n) for n = 1..219</a>
%F A278778 Empirical for column k:
%F A278778 k=1: a(n) = (1/120)*n^5 - (1/24)*n^4 + (1/24)*n^3 + (1/24)*n^2 - (1/20)*n
%F A278778 k=2: [polynomial of degree 10]
%F A278778 k=3: [polynomial of degree 19]
%F A278778 k=4: [polynomial of degree 36]
%F A278778 k=5: [polynomial of degree 69]
%F A278778 k=6: [polynomial of degree 134]
%e A278778 Some solutions for n=4 k=4
%e A278778 ..1..0..0..1. .1..1..0..0. .1..0..0..1. .1..1..1..1. .1..0..0..0
%e A278778 ..1..1..0..1. .1..0..1..1. .1..1..0..0. .1..0..0..0. .0..1..0..1
%e A278778 ..0..1..1..1. .0..1..1..1. .1..1..1..0. .0..1..1..0. .0..1..0..1
%e A278778 ..0..1..1..1. .1..0..1..1. .0..0..1..0. .0..1..1..0. .1..0..0..1
%Y A278778 Column 1 is A000389(n+1).
%K A278778 nonn,tabl
%O A278778 1,5
%A A278778 _R. H. Hardin_, Nov 28 2016