A232941 T(n,k)=Number of nXk 0..2 arrays with no element x(i,j) adjacent to value 2-x(i,j) horizontally, vertically or antidiagonally

3, 6, 6, 12, 12, 12, 24, 26, 26, 24, 48, 56, 84, 56, 48, 96, 120, 252, 252, 120, 96, 192, 258, 774, 1048, 774, 258, 192, 384, 554, 2360, 4458, 4458, 2360, 554, 384, 768, 1190, 7212, 18850, 26644, 18850, 7212, 1190, 768, 1536, 2556, 22024, 79810, 157322, 157322

Offset

1,1

Comments

Table starts

....3....6.....12......24........48.........96..........192...........384

....6...12.....26......56.......120........258..........554..........1190

...12...26.....84.....252.......774.......2360.........7212.........22024

...24...56....252....1048......4458......18850........79810........337850

...48..120....774....4458.....26644.....157322.......932576.......5521380

...96..258...2360...18850....157322....1294504.....10700160......88318190

..192..554...7212...79810....932576...10700160....123516664....1422959686

..384.1190..22024..337850...5521380...88318190...1422959686...22870954236

..768.2556..67272.1430144..32701386..729295244..16403819514..367894792064

.1536.5490.205466.6054098.193661452.6021446660.189062126148.5916284262276

Links

R. H. Hardin, Table of n, a(n) for n = 1..924

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3)

k=3: a(n) = a(n-1) +5*a(n-2) +4*a(n-3) -a(n-5) for n>6

k=4: [order 8] for n>9

k=5: [order 13] for n>14

k=6: [order 21] for n>22

k=7: [order 34] for n>35

Example

Some solutions for n=5 k=4
..1..2..2..1....2..2..2..2....2..2..2..2....1..0..1..0....2..2..2..2
..2..2..2..2....2..2..2..1....2..2..1..2....0..0..0..1....2..2..2..2
..2..2..2..2....1..2..2..2....2..2..2..2....0..0..0..0....2..2..2..1
..2..1..2..1....2..2..2..2....1..2..2..2....1..0..0..1....2..2..2..2
..2..2..2..2....2..1..2..1....2..1..2..2....0..1..0..0....2..1..2..2

Crossrefs

Column 1 is A003945

Sequence in context: A160713 A279625 A012212 * A080866 A310131 A066393

Adjacent sequences: A232938 A232939 A232940 * A232942 A232943 A232944

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 02 2013

Status

approved