A201353 T(n,k)=Number of nXk 0..1 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor

0, 2, 2, 2, 4, 2, 3, 8, 8, 3, 4, 14, 18, 14, 4, 5, 23, 47, 47, 23, 5, 6, 36, 118, 191, 118, 36, 6, 7, 54, 273, 752, 752, 273, 54, 7, 8, 78, 585, 2732, 4860, 2732, 585, 78, 8, 9, 109, 1174, 9111, 29540, 29540, 9111, 1174, 109, 9, 10, 148, 2228, 28011, 164704, 310036, 164704

Offset

1,2

Comments

Table starts

.0...2....2......3........4..........5............6..............7

.2...4....8.....14.......23.........36...........54.............78

.2...8...18.....47......118........273..........585...........1174

.3..14...47....191......752.......2732.........9111..........28011

.4..23..118....752.....4860......29540.......164704.........838248

.5..36..273...2732....29540.....310036......3030673.......27104947

.6..54..585...9111...164704....3030673.....53350918......867792264

.7..78.1174..28011...838248...27104947....867792264....26097731070

.8.109.2228..79918..3906802..220732437..12855063828...718921134406

.9.148.4030.213153.16781171.1641106829.173064550218.17996760930623

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical: T(n,k) is a polynomial in n of degree 2^k-1 for n>2,1,1,4,10,22,46 for k in 1..7

Example

Some solutions for n=10 k=3
..0..0..1....0..0..0....0..0..0....0..1..1....0..0..0....0..0..0....0..0..0
..0..0..1....0..0..0....0..0..1....0..1..1....0..1..1....0..0..0....0..0..0
..0..1..1....0..0..0....0..0..1....0..1..1....0..1..1....0..0..0....0..0..0
..0..1..1....0..1..1....0..0..1....0..1..1....0..1..1....0..0..1....0..0..0
..0..1..1....1..0..0....0..1..1....0..1..1....1..0..0....0..1..1....0..0..1
..1..0..0....1..0..1....0..1..1....0..1..1....1..0..1....1..0..0....0..1..1
..1..1..0....1..0..1....0..1..1....1..0..0....1..0..1....1..0..0....1..0..1
..1..1..0....1..1..1....1..0..0....1..1..1....1..0..1....1..1..0....1..0..1
..1..1..1....1..1..1....1..0..1....1..1..1....1..0..1....1..1..0....1..0..1
..1..1..1....1..1..1....1..1..1....1..1..1....1..1..1....1..1..0....1..1..1

Crossrefs

Sequence in context: A108920 A079405 A332347 * A072048 A161841 A335901

Adjacent sequences: A201350 A201351 A201352 * A201354 A201355 A201356

Keyword

nonn,tabl

Author

R. H. Hardin Nov 30 2011

Status

approved