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%I #11 Mar 19 2017 01:11:53
%S 3,5,8,15,27,60,123,285,648,1529,3603,8680,20883,50825,124056,304575,
%T 750123,1855100,4600203,11442087,28527448,71292605,178526883,
%U 447919420,1125750147,2833906685,7144450568,18036423975,45591631803,115381823348
%N Number of 2n-bead necklaces labeled with numbers 1..4 not allowing reversal, with neighbors differing by exactly 1.
%H Andrew Howroyd, <a href="/A208723/b208723.txt">Table of n, a(n) for n = 1..100</a>
%F a(n) = (1/n) * Sum_{d | n} totient(n/d) * A005248(d). - _Andrew Howroyd_, Mar 18 2017
%e All solutions for n=4:
%e ..1....1....3....2....1....2....2....2....2....1....1....1....1....1....1
%e ..2....2....4....3....2....3....3....3....3....2....2....2....2....2....2
%e ..1....3....3....2....3....2....4....4....2....3....1....1....3....3....1
%e ..2....4....4....3....2....3....3....3....3....2....2....2....4....2....2
%e ..3....3....3....2....1....2....4....2....4....3....1....3....3....3....1
%e ..2....4....4....3....2....3....3....3....3....4....2....4....2....2....2
%e ..3....3....3....2....3....4....4....4....4....3....1....3....3....3....3
%e ..2....2....4....3....2....3....3....3....3....2....2....2....2....2....2
%Y Column 4 of A208727.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 01 2012
%E a(26)-a(30) from _Andrew Howroyd_, Mar 18 2017
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