A221459 T(n,k)=Number of 0..k arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..k order

0, 0, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 2, 6, 3, 0, 1, 2, 7, 16, 5, 0, 1, 2, 7, 24, 44, 8, 0, 1, 2, 7, 25, 88, 120, 13, 0, 1, 2, 7, 25, 101, 328, 328, 21, 0, 1, 2, 7, 25, 102, 436, 1235, 896, 34, 0, 1, 2, 7, 25, 102, 455, 1971, 4668, 2448, 55, 0, 1, 2, 7, 25, 102, 456, 2192, 9159, 17675

Offset

1,9

Comments

Table starts

..0.....0......0......0.......0.......0.......0.......0.......0.......0.......0

..1.....1......1......1.......1.......1.......1.......1.......1.......1.......1

..1.....2......2......2.......2.......2.......2.......2.......2.......2.......2

..2.....6......7......7.......7.......7.......7.......7.......7.......7.......7

..3....16.....24.....25......25......25......25......25......25......25......25

..5....44.....88....101.....102.....102.....102.....102.....102.....102.....102

..8...120....328....436.....455.....456.....456.....456.....456.....456.....456

.13...328...1235...1971....2192....2218....2219....2219....2219....2219....2219

.21...896...4668...9159...11203...11605...11639...11640...11640...11640...11640

.34..2448..17675..43262...59814...64647...65320...65363...65364...65364...65364

.55..6688..66974.206285..329343..379349..389533..390592..390645..390646..390646

.89.18272.253858.988963.1851911.2320555.2451393.2471066.2472654.2472718.2472719

Links

R. H. Hardin, Table of n, a(n) for n = 1..2080

Example

Some solutions for n=6 k=4
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1
..2....2....2....2....1....0....0....2....2....2....1....1....2....2....2....1
..3....3....1....2....2....2....2....3....2....1....2....2....2....0....1....0
..4....3....0....1....2....0....3....1....3....3....0....3....0....2....2....1
..1....4....3....3....3....3....2....0....1....0....1....2....3....1....1....0

Crossrefs

Column 1 is A000045(n-1)

Column 2 is A002605(n-1)

Sequence in context: A163000 A303548 A105524 * A166387 A000209 A359901

Adjacent sequences: A221456 A221457 A221458 * A221460 A221461 A221462

Keyword

nonn,tabl

Author

R. H. Hardin Jan 17 2013

Status

approved