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%I #11 Mar 20 2017 09:50:13
%S 3,5,8,14,24,47,89,187,396,881,1990,4645,10935,26211,63320,154378,
%T 378444,933023,2308957,5735372,14286908,35683815,89324138,224057919,
%U 563033979,1417210457,3572641304,9018885122,22796905056,57692673963,146167385345,370710166435
%N Number of 2n-bead necklaces labeled with numbers 1..4 allowing reversal, with neighbors differing by exactly 1.
%H Andrew Howroyd, <a href="/A208667/b208667.txt">Table of n, a(n) for n = 1..100</a>
%F a(n) = (2*A208723(n) + A090991(n))/4. - _Andrew Howroyd_, Mar 19 2017
%e All solutions for n=4:
%e ..1....2....2....2....1....1....1....1....1....3....1....1....2....2
%e ..2....3....3....3....2....2....2....2....2....4....2....2....3....3
%e ..1....2....2....2....1....1....3....3....3....3....3....1....4....4
%e ..2....3....3....3....2....2....4....2....2....4....2....2....3....3
%e ..1....4....2....2....3....1....3....1....3....3....3....3....2....4
%e ..2....3....3....3....4....2....4....2....4....4....2....2....3....3
%e ..1....4....2....4....3....3....3....3....3....3....3....3....4....4
%e ..2....3....3....3....2....2....2....2....2....4....2....2....3....3
%Y Column 4 of A208671.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 29 2012
%E a(25)-a(32) from _Andrew Howroyd_, Mar 19 2017
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