

A330620


Number of length n necklaces with entries covering an initial interval of positive integers and no adjacent entries equal.


2



0, 1, 2, 10, 54, 392, 3378, 34120, 393738, 5112406, 73756026, 1170482186, 20263782630, 380047964920, 7676106365966, 166114208828980, 3834434324386350, 94042629535109500, 2442147034719168714, 66942194906112161302, 1931543452345335094678, 58519191359163454708564
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OFFSET

1,3


LINKS



EXAMPLE

Case n=4: there are the following 10 necklaces:
1212,
1213, 1232, 1323,
1234, 1243, 1324, 1342, 1423, 1432.


PROG

(PARI) \\ here U(n, k) is A208535(n, k) for n > 1.
U(n, k)={sumdiv(n, d, eulerphi(n/d)*(k1)^d)/n  if(n%2, k1)}
a(n)={if(n<1, n==0, sum(j=1, n, U(n, j)*sum(k=j, n, (1)^(kj)*binomial(k, j))))}


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



