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Search: id:A120766
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| A120766 |
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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. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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1,3
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FORMULA
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For n>=3, a(n)=2+2*Sum_{k=2..[n/2]} (C(n-k,k) + C(n-k-1,k-1))*A061714(k)
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PROGRAM
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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)) ) ) }
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CROSSREFS
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Adjacent sequences: A120763 A120764 A120765 this_sequence A120767 A120768 A120769
Sequence in context: A076278 A099576 A026549 this_sequence A121404 A074442 A123045
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KEYWORD
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nonn
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AUTHOR
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Max Alekseyev (maxal(AT)cs.ucsd.edu), Jul 03 2006
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