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Number of 2n-bead necklaces labeled with numbers 1..7 allowing reversal, with neighbors differing by exactly 1.
1

%I #9 Mar 22 2017 22:05:40

%S 6,11,20,41,86,208,514,1398,3934,11576,34850,107303,334396,1053851,

%T 3345320,10685570,34292064,110498897,357256018,1158492478,3766458404,

%U 12274037845,40082339406,131144365904,429838330172,1411104048106,4639351259122,15273992343065

%N Number of 2n-bead necklaces labeled with numbers 1..7 allowing reversal, with neighbors differing by exactly 1.

%H Andrew Howroyd, <a href="/A208670/b208670.txt">Table of n, a(n) for n = 1..100</a>

%F a(n) = (2*A208726(n) + A129639(11+n))/4.

%e All solutions for n=3:

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

%e ..2....6....2....6....4....5....2....7....5....2....3....3....5....6....4....5

%e ..1....5....3....7....3....4....1....6....6....3....4....2....6....5....5....4

%e ..2....6....2....6....4....5....2....7....5....4....3....3....7....6....4....5

%e ..3....5....3....7....5....6....1....6....6....3....4....2....6....7....5....4

%e ..2....6....2....6....4....5....2....7....5....2....3....3....5....6....4....5

%e ..

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

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

%e ..2....4....3....5

%e ..3....5....4....6

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

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

%Y Column 7 of A208671.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 29 2012

%E a(12)-a(28) from _Andrew Howroyd_, Mar 19 2017