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A000264
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Number of 3-edge-connected rooted cubic maps with 2n nodes and a distinguished Hamilton cycle
(Formerly M2974 N1203)
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3
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1, 1, 3, 14, 80, 518, 3647, 27274, 213480, 1731652, 14455408, 123552488, 1077096124, 9548805240, 85884971043, 782242251522, 7203683481720, 66989439309452, 628399635777936, 5940930064989720, 56562734108608536
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
W. T. Tutte, A census of Hamiltonian polygons, Canad. J. Math., 14 (1962), 402-417.
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FORMULA
| Let b(n)=(2n)!*(2n+2)!/(2*n!*(n+1)!^2*(n+2)!). Let B(x) be the generating function producing b(n), and A(x) be the generating function producing a(n). Then these sequences satisfy the functional equation B(x)=A(x(1+2*B(x))^2). [From Sean A. Irvine (sairvin(AT)xtra.co.nz), Apr 05 2010]
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CROSSREFS
| Cf. A000309, A000356, A004304.
Sequence in context: A168592 A121873 A107596 * A009053 A202474 A077054
Adjacent sequences: A000261 A000262 A000263 * A000265 A000266 A000267
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Better definition from Michael Albert, Oct 24 2008
More terms from Sean A. Irvine (sairvin(AT)xtra.co.nz), Apr 05 2010
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