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 A000264 Number of 3-edge-connected rooted cubic maps with 2n nodes and a distinguished Hamiltonian cycle. (Formerly M2974 N1203) 4
 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; text; internal format)
 OFFSET 1,3 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). LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..200 L. B. Richmond, On Hamiltonian polygons, J. Combinatorial Theory Ser. B 21 (1976), no. 1, 81--87. MR0432491 (55 #5479) [See v_n]. W. T. Tutte, A census of Hamiltonian polygons, Canad. J. Math., 14 (1962), 402-417. 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). - Sean A. Irvine, Apr 05 2010 MATHEMATICA max = 21; b[n_] := (2n)!*(2n + 2)!/(2*n!*(n + 1)!^2*(n + 2)!); b[0] = 0; bf[x_] := Sum[b[n]*x^n, {n, 0, max}]; Clear[a]; a[0] = 0; a[1] = a[2] = 1; af[x_] := Sum[a[n]*x^n, {n, 0, max}]; se = Series[bf[x] - af[x*(1 + 2*bf[x])^2], {x, 0, max}] // Normal; Table[a[n], {n, 1, max}] /. SolveAlways[se == 0, x] // First (* Jean-François Alcover, Jan 31 2013, after Sean A. Irvine *) CROSSREFS Cf. A000309, A000356, A004304. Sequence in context: A121873 A107596 A212391 * A009053 A202474 A256336 Adjacent sequences:  A000261 A000262 A000263 * A000265 A000266 A000267 KEYWORD nonn,nice AUTHOR EXTENSIONS Better definition from Michael Albert, Oct 24 2008 More terms from Sean A. Irvine, Apr 05 2010 STATUS approved

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Last modified October 18 08:08 EDT 2019. Contains 328146 sequences. (Running on oeis4.)