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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
7

%I #4 Jan 17 2013 08:37:32

%S 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,

%T 25,88,120,13,0,1,2,7,25,101,328,328,21,0,1,2,7,25,102,436,1235,896,

%U 34,0,1,2,7,25,102,455,1971,4668,2448,55,0,1,2,7,25,102,456,2192,9159,17675

%N 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

%C Table starts

%C ..0.....0......0......0.......0.......0.......0.......0.......0.......0.......0

%C ..1.....1......1......1.......1.......1.......1.......1.......1.......1.......1

%C ..1.....2......2......2.......2.......2.......2.......2.......2.......2.......2

%C ..2.....6......7......7.......7.......7.......7.......7.......7.......7.......7

%C ..3....16.....24.....25......25......25......25......25......25......25......25

%C ..5....44.....88....101.....102.....102.....102.....102.....102.....102.....102

%C ..8...120....328....436.....455.....456.....456.....456.....456.....456.....456

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

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

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

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

%C .89.18272.253858.988963.1851911.2320555.2451393.2471066.2472654.2472718.2472719

%H R. H. Hardin, <a href="/A221459/b221459.txt">Table of n, a(n) for n = 1..2080</a>

%e Some solutions for n=6 k=4

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1

%e ..2....2....2....2....1....0....0....2....2....2....1....1....2....2....2....1

%e ..3....3....1....2....2....2....2....3....2....1....2....2....2....0....1....0

%e ..4....3....0....1....2....0....3....1....3....3....0....3....0....2....2....1

%e ..1....4....3....3....3....3....2....0....1....0....1....2....3....1....1....0

%Y Column 1 is A000045(n-1)

%Y Column 2 is A002605(n-1)

%K nonn,tabl

%O 1,9

%A _R. H. Hardin_ Jan 17 2013