%I #9 Jan 09 2020 19:36:43
%S 0,1,2,10,54,392,3378,34120,393738,5112406,73756026,1170482186,
%T 20263782630,380047964920,7676106365966,166114208828980,
%U 3834434324386350,94042629535109500,2442147034719168714,66942194906112161302,1931543452345335094678,58519191359163454708564
%N Number of length n necklaces with entries covering an initial interval of positive integers and no adjacent entries equal.
%H Andrew Howroyd, <a href="/A330620/b330620.txt">Table of n, a(n) for n = 1..200</a>
%e Case n=4: there are the following 10 necklaces:
%e 1212,
%e 1213, 1232, 1323,
%e 1234, 1243, 1324, 1342, 1423, 1432.
%o (PARI) \\ here U(n, k) is A208535(n, k) for n > 1.
%o U(n, k)={sumdiv(n, d, eulerphi(n/d)*(k-1)^d)/n - if(n%2, k-1)}
%o a(n)={if(n<1, n==0, sum(j=1, n, U(n,j)*sum(k=j, n, (-1)^(k-j)*binomial(k, j))))}
%Y Row sums of A330618.
%Y Cf. A019536, A208535.
%K nonn
%O 1,3
%A _Andrew Howroyd_, Dec 20 2019