A219502 T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 nXk array

2, 2, 2, 3, 3, 3, 4, 5, 5, 4, 5, 7, 11, 7, 5, 6, 9, 18, 18, 9, 6, 7, 11, 26, 35, 26, 11, 7, 8, 13, 35, 58, 58, 35, 13, 8, 9, 15, 45, 88, 107, 88, 45, 15, 9, 10, 17, 56, 126, 179, 179, 126, 56, 17, 10, 11, 19, 68, 173, 281, 325, 281, 173, 68, 19, 11, 12, 21, 81, 230, 421, 550, 550, 421

Offset

1,1

Comments

Table starts

..2..2...3...4....5....6.....7.....8.....9....10....11....12....13....14....15

..2..3...5...7....9...11....13....15....17....19....21....23....25....27....29

..3..5..11..18...26...35....45....56....68....81....95...110...126...143...161

..4..7..18..35...58...88...126...173...230...298...378...471...578...700...838

..5..9..26..58..107..179...281...421...608...852..1164..1556..2041..2633..3347

..6.11..35..88..179..325...550...885..1369..2050..2986..4246..5911..8075.10846

..7.13..45.126..281..550...995..1703..2793..4424..6804.10200.14949.21470.30277

..8.15..56.173..421..885..1703..3083..5328..8869.14306.22458.34423.51649.76017

..9.17..68.230..608.1369..2793..5328..9663.16831.28346.46382.74003

.10.19..81.298..852.2050..4424..8869.16831.30581.53601.91116

.11.21..95.378.1164.2986..6804.14306.28346.53601.97541

.12.23.110.471.1556.4246.10200.22458.46382.91116

Links

R. H. Hardin, Table of n, a(n) for n = 1..239

Formula

Empirical for column k:

k=1: a(n) = n for n>1

k=2: a(n) = 2*n - 1 for n>1

k=3: a(n) = (1/2)*n^2 + (7/2)*n - 4 for n>1

k=4: a(n) = (1/6)*n^3 + n^2 + (23/6)*n - 7 for n>2

k=5: a(n) = (1/24)*n^4 + (1/4)*n^3 + (35/24)*n^2 + (21/4)*n - 13 for n>2

k=6: a(n) = (1/120)*n^5 + (1/24)*n^4 + (13/24)*n^3 + (59/24)*n^2 + (59/20)*n - 17 for n>3

k=7: a(n) = (1/720)*n^6 + (1/240)*n^5 + (23/144)*n^4 + (13/16)*n^3 + (331/180)*n^2 + (311/60)*n - 27 for n>3

Example

Some solutions for n=3 k=4
..0..0..0..0....0..0..0..0....0..0..0..0....1..0..0..0....1..0..0..0
..0..0..0..0....0..0..0..0....1..0..0..0....1..1..0..0....1..0..0..0
..1..0..0..0....1..1..1..0....1..1..1..0....1..1..1..0....1..0..0..0

Crossrefs

Column 1 is A000027

Column 2 is A004273

Column 3 is A056000(n-1) for n>1

Sequence in context: A199575 A120187 A029062 * A219704 A253144 A265410

Adjacent sequences: A219499 A219500 A219501 * A219503 A219504 A219505

Keyword

nonn,tabl

Author

R. H. Hardin Nov 20 2012

Status

approved