A330621 Number of length n bracelets with entries covering an initial interval of positive integers and no adjacent entries equal.

0, 1, 1, 7, 27, 207, 1689, 17137, 196869, 2556856, 36878013, 585247590, 10131891315, 190024056601, 3838053182983, 83057105368627, 1917217162193175, 47021314781221603, 1221073517359584357, 33471097453271690668, 965771726172667547339, 29259595679585441629303

Offset: 1

Author

Andrew Howroyd, Dec 20 2019

Keywords

• nonn

Examples

			Case n=4: there are the following 7 bracelets:
  1212,
  1213, 1232, 1323,
  1234, 1243, 1324.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200

Crossrefs

Row sums of A330341.

Cf. A208544.

Programs

PARI

\\ here U(n, k) is A208544(n, k) for n > 1.
U(n, k) = (sumdiv(n, d, eulerphi(n/d)*(k-1)^d)/n + if(n%2, 1-k, k*(k-1)^(n/2)/2))/2;
a(n)={if(n<1, n==0, sum(j=1, n, U(n,j)*sum(k=j, n, (-1)^(k-j)*binomial(k, j))))}