A278807 T(n,k)=Number of nXk 0..2 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order.

3, 6, 6, 10, 22, 10, 15, 63, 63, 15, 21, 154, 322, 154, 21, 28, 336, 1439, 1439, 336, 28, 36, 672, 5767, 12958, 5767, 672, 36, 45, 1254, 20972, 110455, 110455, 20972, 1254, 45, 55, 2211, 69834, 870473, 2179956, 870473, 69834, 2211, 55, 66, 3718, 214774, 6275546

Offset

1,1

Comments

Table starts

..3....6......10.........15............21...............28.................36

..6...22......63........154...........336..............672...............1254

.10...63.....322.......1439..........5767............20972..............69834

.15..154....1439......12958........110455...........870473............6275546

.21..336....5767.....110455.......2179956.........41299256..........725674326

.28..672...20972.....870473......41299256.......1976588468........89730161098

.36.1254...69834....6275546.....725674326......89730161098.....10811999412826

.45.2211..214774...41370842...11698232451....3776527762052...1224101415304069

.55.3718..615120..250517485..172994405326..146582077597322.128795068372302728

.66.6006.1653047.1402100369.2356249442222.5255148833158068

Links

R. H. Hardin, Table of n, a(n) for n = 1..127

Formula

Empirical for column k:

k=1: a(n) = (1/2)*n^2 + (3/2)*n + 1

k=2: [polynomial of degree 6]

k=3: [polynomial of degree 16]

k=4: [polynomial of degree 44]

Example

Some solutions for n=4 k=4
..1..0..0..0. .1..0..0..0. .1..1..1..0. .1..1..0..0. .1..1..0..0
..1..1..1..0. .1..1..1..0. .2..0..0..2. .2..1..2..2. .2..1..2..2
..1..2..1..0. .1..2..0..1. .2..1..0..0. .2..2..1..1. .2..2..1..0
..2..0..1..2. .1..2..0..1. .2..1..0..2. .2..2..2..2. .2..2..1..1

Crossrefs

Diagonal is A229770.

Column 1 is A000217(n+1).

Column 2 is A257200(n+1).

Sequence in context: A147849 A332546 A002853 * A340620 A184137 A135610

Adjacent sequences: A278804 A278805 A278806 * A278808 A278809 A278810

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 28 2016

Status

approved