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

Author

R. H. Hardin Nov 20 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000027

Column 2 is A004273

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

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