A120766 Number of ways to seat n people around a circular table such that person i is next to person i-1 or i+1 or both.

1, 1, 2, 6, 12, 36, 86, 270, 746, 2554, 8032, 29716, 103482, 409242, 1550850, 6508702, 26509428, 117368404, 508962350, 2365560998, 10842378698, 52685516658, 253754085960, 1284660919140, 6471281910962, 34031293950258

Offset

1,3

Links

Table of n, a(n) for n=1..26.

Formula

For n>=3, a(n)=2+2*Sum_{k=2..[n/2]} (C(n-k,k) + C(n-k-1,k-1))*A061714(k)

Prog

(PARI) { a(n) = if(n<3, 1, 2 + 2*sum(k=2, n\2, (binomial(n-k, k)+binomial(n-k-1, k-1)) * ((-1)^k+sum(i=0, k-1, (-1)^(k-1-i)*binomial(k, i+1)*i!*2^i)) ) ) }

Crossrefs

Sequence in context: A347452 A307015 A026549 * A121404 A202337 A189854

Adjacent sequences: A120763 A120764 A120765 * A120767 A120768 A120769

Keyword

nonn

Author

Max Alekseyev, Jul 03 2006

Status

approved