Search: id:A000168
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%I A000168 M1940 N0768
%S A000168 1,2,9,54,378,2916,24057,208494,1876446,17399772,165297834,1602117468,
%T A000168 15792300756,157923007560,1598970451545,16365932856990,169114639522230,
%U A000168 1762352559231660,18504701871932430,195621134074714260
%N A000168 2*3^n*(2*n)!/(n!*(n+2)!).
%C A000168 Number of rooted 4-regular planar maps with n vertices.
%C A000168 Also, number of doodles with n crossings, irrespective of the number 
               of loops.
%D A000168 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000168 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000168 R. Cori and B. Vauquelin, Planar maps are well labeled trees, Canad. 
               J. Math., 33 (1981), 1023-1042.
%D A000168 J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 
               2004; p. 714.
%D A000168 V. A. Liskovets, A census of nonisomorphic planar maps, in Algebraic 
               Methods in Graph Theory, Vol. II, ed. L. Lovasz and V. T. Sos, North-Holland, 
               1981.
%D A000168 V. A. Liskovets, Enumeration of nonisomorphic planar maps, Selecta Math. 
               Sovietica, 4 (No. 4, 1985), 303-323.
%D A000168 R. C. Mullin, On the average activity of a spanning tree of a rooted 
               map, J. Combin. Theory, 3 (1967), 103-121.
%D A000168 W. T. Tutte, A census of planar maps, Canad. J. Math., 15 (1963), 249-271.
%H A000168 T. D. Noe, <a href="b000168.txt">Table of n, a(n) for n=0..100</a>
%H A000168 M. Bousquet-Melou, <a href="http://arXiv.org/abs/math.CO/0501266">Limit 
               laws for embedded trees</a>
%H A000168 M. Bousqet-Melou and A. Jehanne, <a href="http://arXiv.org/abs/math.CO/
               0504018">Polynomial equations with one catalytic variable, algebraic 
               series and map enumeration</a>
%H A000168 G. Schaeffer and P. Zinn-Justin, <a href="http://arXiv.org/abs/math-ph/
               0304034">On the asymptotic number of plane curves and alternating 
               knots</a>
%H A000168 P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/
               Publications/books.html">Analytic Combinatorics</a>, 2009; see page 
               516
%F A000168 G.f. satisfies A(z) = 1 - 16z +18zA - 27z^2A^2.
%F A000168 G.f.: F(1/2,1;3;12x). [From Paul Barry (pbarry(AT)wit.ie), Feb 04 2009]
%F A000168 a(n)=2*3^n*A000108(n)/(n+2). [From Paul Barry (pbarry(AT)wit.ie), Feb 
               04 2009]
%p A000168 f:=n->2*3^n*(2*n)!/(n!*(n+2)!);
%Y A000168 First row of array A102994. Cf. A005470.
%Y A000168 Sequence in context: A074602 A073986 A089436 this_sequence A127128 A064151 
               A075679
%Y A000168 Adjacent sequences: A000165 A000166 A000167 this_sequence A000169 A000170 
               A000171
%K A000168 nonn,nice,easy
%O A000168 0,2
%A A000168 N. J. A. Sloane (njas(AT)research.att.com).

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