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Number of nonnegative integer arrays of length n+13 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value 7.
1

%I #6 Oct 01 2021 16:38:57

%S 1,15,149,1173,7996,49210,280751,1510267,7752966,38313584,183476493,

%T 855810005,3904023943,17474944971,76959615336,334220597220,

%U 1434013918092,6088757186340,25619291046722,106954200571650,443491592171780

%N Number of nonnegative integer arrays of length n+13 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value 7.

%C Column 6 of A211849.

%H R. H. Hardin, <a href="/A211847/b211847.txt">Table of n, a(n) for n = 1..210</a>

%e Some solutions for n=3

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

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

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

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

%e ..3....2....3....3....3....3....3....2....3....2....2....2....3....3....2....3

%e ..2....3....3....3....3....3....3....3....3....2....2....3....3....2....3....3

%e ..3....3....4....4....3....3....4....3....4....3....3....3....4....2....3....4

%e ..3....4....4....4....4....3....4....4....4....3....3....4....4....4....4....3

%e ..4....4....5....4....4....4....1....4....4....4....4....4....5....4....4....4

%e ..4....5....5....5....5....4....1....4....5....4....4....4....4....5....5....4

%e ..5....5....3....5....5....5....5....5....5....5....5....5....4....5....5....5

%e ..5....5....3....5....6....5....5....5....6....5....5....5....6....6....6....5

%e ..6....6....6....6....6....6....6....6....6....6....6....6....6....5....6....6

%e ..6....6....6....6....6....6....6....6....6....6....6....6....7....5....7....6

%e ..7....7....7....7....7....7....7....7....7....7....7....7....6....7....6....7

%Y Cf. A211849.

%K nonn

%O 1,2

%A _R. H. Hardin_ Apr 22 2012