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A278363
T(n,k)=Number of nXk 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly one mistake.
8
0, 1, 1, 4, 6, 4, 10, 27, 27, 10, 20, 96, 142, 96, 20, 35, 281, 701, 701, 281, 35, 56, 708, 3183, 4872, 3183, 708, 56, 84, 1590, 12875, 34038, 34038, 12875, 1590, 84, 120, 3264, 46236, 229887, 366982, 229887, 46236, 3264, 120, 165, 6237, 149099, 1429751
OFFSET
1,4
COMMENTS
Table starts
...0.....1.......4........10..........20............35...............56
...1.....6......27........96.........281...........708.............1590
...4....27.....142.......701........3183.........12875............46236
..10....96.....701......4872.......34038........229887..........1429751
..20...281....3183.....34038......366982.......4058169.........44208465
..35...708...12875....229887.....4058169......72941420.......1349344763
..56..1590...46236...1429751....44208465....1349344763......41820621848
..84..3264..149099...8023290...451571539...24833319003....1335072188627
.120..6237..438091..40628537..4213513472..434369879650...42737962734110
.165.11242.1188762.187182375.35702217342.7020524920612.1315545171895930
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = (1/6)*n^3 - (1/6)*n
k=2: [polynomial of degree 7]
k=3: [polynomial of degree 15]
k=4: [polynomial of degree 31]
k=5: [polynomial of degree 63]
k=6: [polynomial of degree 127]
EXAMPLE
Some solutions for n=4 k=4
..0..1..1..1. .0..1..1..1. .0..1..1..1. .0..0..1..1. .0..0..1..1
..1..0..0..1. .0..1..1..1. .1..0..0..1. .1..0..0..0. .0..0..0..1
..1..1..1..1. .0..0..1..1. .0..0..0..1. .1..0..0..0. .0..0..1..0
..0..0..1..0. .1..0..0..1. .1..0..0..0. .1..1..0..0. .0..1..1..1
CROSSREFS
Column 1 is A000292(n-1).
Sequence in context: A277278 A328722 A143521 * A123969 A255679 A019188
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 19 2016
STATUS
approved