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Number of length-(n+1) 0..7 arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.
1

%I #4 Feb 01 2016 10:25:28

%S 2,4,11,33,114,435,1829,8376,41466,220115,1242614,7395663,45999012,

%T 296480813,1965371333,13314182333,91697130971,639451012407,

%U 4501167824269,31908164747227,227399949031725,1627202389749190,11680282747792917

%N Number of length-(n+1) 0..7 arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.

%C Column 7 of A268327.

%H R. H. Hardin, <a href="/A268326/b268326.txt">Table of n, a(n) for n = 1..210</a>

%H R. H. Hardin, <a href="/A268326/a268326.txt">Empirical recurrence of order 54</a>

%F Empirical recurrence of order 54 (see link above)

%e Some solutions for n=9

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

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

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

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

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

%e ..5....3....1....3....2....2....2....1....3....4....3....0....2....2....2....0

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

%e ..4....2....1....4....0....4....2....3....3....5....4....0....3....4....2....1

%e ..5....0....5....0....0....1....3....4....2....3....1....3....5....5....1....0

%e ..6....4....4....5....1....5....0....2....3....1....3....4....3....4....2....3

%Y Cf. A268327.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 01 2016