A219816 T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal, vertical or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nXk array

3, 3, 3, 6, 6, 6, 10, 15, 16, 10, 15, 28, 62, 33, 15, 21, 45, 165, 169, 61, 21, 28, 66, 377, 648, 414, 106, 28, 36, 91, 795, 2179, 2237, 987, 176, 36, 45, 120, 1588, 7049, 11395, 7689, 2359, 281, 45, 55, 153, 3039, 22017, 57848, 62341, 27340, 5569, 433, 55, 66, 190

Offset

1,1

Comments

Table starts

..3....3......6......10.......15........21........28........36........45

..3....6.....15......28.......45........66........91.......120.......153

..6...16.....62.....165......377.......795......1588......3039......5612

.10...33....169.....648.....2179......7049.....22017.....65842....188487

.15...61....414....2237....11395.....57848....283334...1322739...5913303

.21..106....987....7689....62341....510090...3967857..29319493.208512645

.28..176...2359...27340...358480...4734774..59065976.707079160

.36..281...5569...97483..2042977..43171729.864699568

.45..433..12737..336348.11133454.376434884

.55..646..27982.1107489.57524941

.66..936..59028.3485470

.78.1321.119947

Links

R. H. Hardin, Table of n, a(n) for n = 1..111

Example

Some solutions for n=3 k=4
..1..1..1..1....1..0..0..0....1..0..0..0....0..0..0..0....1..1..1..1
..2..1..1..1....1..1..0..0....2..1..0..0....0..0..0..0....1..1..0..0
..2..2..2..2....1..1..1..1....2..2..1..0....2..2..1..1....2..2..0..0

Crossrefs

Column 1 and Row 1 are A000217 for n>1

Row 2 is A000384 for n>1

Sequence in context: A080607 A013322 A211534 * A177821 A166273 A244482

Adjacent sequences: A219813 A219814 A219815 * A219817 A219818 A219819

Keyword

nonn,tabl

Author

R. H. Hardin Nov 28 2012

Status

approved