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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 6
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified November 17 16:06 EST 2019. Contains 329240 sequences. (Running on oeis4.)