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%I #12 Mar 12 2017 22:50:26
%S 4,7,10,18,28,56,98,208,418,933,2044,4777,11072,26548,63672,155248,
%T 379348,935278,2311294,5741228,14292966,35699049,89339860,224097602,
%U 563074848,1417313897,3572747650,9019154944,22797181996,57693378135,146168107034,370712004868
%N Number of n-bead necklaces labeled with numbers 1..4 allowing reversal, with no adjacent beads differing by more than 1.
%H Andrew Howroyd, <a href="/A208717/b208717.txt">Table of n, a(n) for n = 1..100</a>
%F a(2n+1) = (1/2) * (A208773(2n+1) + A126358(n+1)). - _Andrew Howroyd_, Mar 03 2017
%F a(2n) = (1/2) * A208773(2n) + (1/4) * (A126358(n) + A126358(n+1)). - _Andrew Howroyd_, Mar 03 2017
%e All solutions for n=3:
%e ..3....2....1....3....4....2....3....1....1....2
%e ..3....2....1....3....4....3....4....1....2....2
%e ..4....2....1....3....4....3....4....2....2....3
%Y Column 4 of A208721.
%Y Cf. A208773, A126358.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 01 2012
%E a(29)-a(32) from _Andrew Howroyd_, Mar 03 2017