A278363 T(n,k)=Number of nXk 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly one mistake.

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

R. H. Hardin, Table of n, a(n) for n = 1..199

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

Adjacent sequences: A278360 A278361 A278362 * A278364 A278365 A278366

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 19 2016

Status

approved