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Search: id:A003436
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| A003436 |
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Number of inequivalent labeled Hamiltonian circuits on n-octahedron. Interlacing chords joining 2n points on circle.
(Formerly M3638)
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+0
5
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| 0, 1, 4, 31, 293, 3326, 44189, 673471, 11588884, 222304897, 4704612119, 108897613826, 2737023412199, 74236203425281, 2161288643251828, 67228358271588991, 2225173863019549229, 78087247031912850686, 2896042595237791161749
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Also called the relaxed menage problem (cf. A000179).
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Bogart, Kenneth P. and Doyle, Peter G., Nonsexist solution of the menage problem, Amer. Math. Monthly 93 (1986), no. 7, 514-519.
M. Hazewinkel and V. V. Kalashnikov, Counting Interlacing Pairs on the Circle, preprint.
D. Singmaster, Hamiltonian circuits on the n-dimensional octahedron. J. Combinatorial Theory Ser. B 19 (1975), no. 1, 1-4.
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FORMULA
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a(n) = (-2n+4)a(n-2) - a(n-3) + (2n+2)a(n-1).
G.f.: x+(1-x)/(1+x)* Sum_{n>=0} A001147(n)*(x/(1+x)^2)^n. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 27 2007
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CROSSREFS
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Equals A003435(n)/(n!*2^n). A003437 gives unlabeled case.
First differences of A000806.
Sequence in context: A039306 A081054 A000858 this_sequence A114475 A076280 A141005
Adjacent sequences: A003433 A003434 A003435 this_sequence A003437 A003438 A003439
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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