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A124353
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Number of (directed) Hamiltonian circuits on the n-antiprism graph.
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3
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6, 18, 32, 58, 112, 220, 450, 938, 1982, 4220, 9022, 19332, 41472, 89022, 191150, 410506, 881656, 1893634, 4067256, 8735972, 18763898, 40302866, 86566390, 185935764, 399371142, 857808780, 1842486536, 3957474934, 8500256470, 18257692546, 39215680080, 84231321290, 180920373632, 388598695916
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The antiprism graph is defined for n>=3; extended to n=1 using the closed form.
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LINKS
| Mordecai J. Golin and Yiu Cho Leung, Unhooking Circulant Graphs: A Combinatorial Method for Counting Spanning Trees, Hamiltonian Cycles and other Parameters. Technical report HKUST-TCSC-2004-02.
Eric Weisstein's World of Mathematics, Antiprism Graph
Eric Weisstein's World of Mathematics, Hamiltonian Cycle
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FORMULA
| a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3) + a(n-5).
a(n) = 2*a(n-1) + a(n-2) - a(n-3) - a(n-4) - 12.
O.g.f.: -18*x^2-6*x-6+(4*x^2+4*x-6)/(x^3+2*x^2+x-1)+4/(x-1)^2+4/(x-1) . - R. J. Mathar, Feb 10 2008
a(n) = 2*(n + 3*A000930(2*n) - 2*A000930(2*n-1)) = A137725(2*n) = 2*A137726(2*n)
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MATHEMATICA
| Table[2 (2 n + RootSum[-1 - 2 # - #^2 + #^3 &, #^n &]), {n, 20}]
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CROSSREFS
| Cf. A124352.
Sequence in context: A030568 A017593 A096286 * A153126 A110671 A134078
Adjacent sequences: A124350 A124351 A124352 * A124354 A124355 A124356
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), Oct 27, 2006
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EXTENSIONS
| Formulas and further terms from Max Alekseyev (maxale(AT)gmail.com), Feb 8, 2008
Typo in formula corrected by Max Alekseyev (maxale(AT)gmail.com), Nov 03 2010
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