A330620 Number of length n necklaces with entries covering an initial interval of positive integers and no adjacent entries equal.

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

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: A369263 A365879 A202365 * A268556 A371816 A175935

Adjacent sequences: A330617 A330618 A330619 * A330621 A330622 A330623

Keyword

nonn

Author

Andrew Howroyd, Dec 20 2019

Status

approved