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 A208723 Number of 2n-bead necklaces labeled with numbers 1..4 not allowing reversal, with neighbors differing by exactly 1. 2

%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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Last modified September 13 07:34 EDT 2024. Contains 375872 sequences. (Running on oeis4.)