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
Keywords
Programs
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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)) ) ) }
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)