A278676 T(n,k)=Number of nXk 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly one mistake.

0, 1, 1, 4, 8, 4, 10, 33, 33, 10, 20, 99, 158, 99, 20, 35, 245, 579, 579, 245, 35, 56, 532, 1801, 2650, 1801, 532, 56, 84, 1050, 4999, 10584, 10584, 4999, 1050, 84, 120, 1926, 12727, 38848, 55854, 38848, 12727, 1926, 120, 165, 3333, 30218, 134265, 280616

Offset

1,4

Comments

Table starts

...0....1......4......10........20.........35...........56.............84

...1....8.....33......99.......245........532.........1050...........1926

...4...33....158.....579......1801.......4999........12727..........30218

..10...99....579....2650.....10584......38848.......134265.........441349

..20..245...1801...10584.....55854.....280616......1378241........6654535

..35..532...4999...38848....280616....1998526.....14437336......106388729

..56.1050..12727..134265...1378241...14437336....157706284.....1809189550

..84.1926..30218..441349...6654535..106388729...1809189550....32788533228

.120.3333..67651.1384443..31404174..791018703..21622163723...632621335872

.165.5500.143936.4148373.143558071.5827280865.263667893290.12823358704308

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

Formula

Empirical for column k:

k=1: a(n) = (1/6)*n^3 - (1/6)*n

k=2: [polynomial of degree 6]

k=3: [polynomial of degree 11]

k=4: [polynomial of degree 20]

k=5: [polynomial of degree 37]

k=6: [polynomial of degree 70]

Example

Some solutions for n=4 k=4
..0..0..1..0. .0..1..0..0. .1..1..0..0. .0..0..1..0. .0..0..0..0
..1..0..1..1. .0..1..1..0. .0..0..0..0. .1..1..0..0. .0..1..1..0
..1..1..0..1. .1..0..0..1. .0..0..1..0. .1..1..1..0. .0..1..1..1
..1..1..1..1. .1..0..1..1. .1..0..1..1. .1..1..1..1. .1..1..1..0

Crossrefs

Column 1 is A000292(n-1).

Sequence in context: A141402 A276619 A145900 * A010298 A196177 A059159

Adjacent sequences: A278673 A278674 A278675 * A278677 A278678 A278679

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 25 2016

Status

approved