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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..200 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)*(k-1)^d)/n - if(n%2, k-1)} a(n)={if(n<1, n==0, sum(j=1, n, U(n, j)*sum(k=j, n, (-1)^(k-j)*binomial(k, j))))} CROSSREFS Row sums of A330618. Cf. A019536, A208535. Sequence in context: A152395 A365879 A202365 * A268556 A175935 A216721 Adjacent sequences: A330617 A330618 A330619 * A330621 A330622 A330623 KEYWORD nonn AUTHOR Andrew Howroyd, Dec 20 2019 STATUS approved

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Last modified December 7 18:28 EST 2023. Contains 367660 sequences. (Running on oeis4.)