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

1,4

Links

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

Example

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

Prog

(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))))}

Crossrefs

Row sums of A330341.

Cf. A208544.

Sequence in context: A192250 A035081 A193257 * A173193 A196323 A003148

Adjacent sequences: A330618 A330619 A330620 * A330622 A330623 A330624

Keyword

nonn

Author

Andrew Howroyd, Dec 20 2019

Status

approved