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

Author

R. H. Hardin Jan 17 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000045(n-1)

Column 2 is A002605(n-1)