Search: id:A000087
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%I A000087 M1240 N0474
%S A000087 2,1,2,4,10,37,138,628,2972,14903,76994,409594,2222628,12281570,
%T A000087 68864086,391120036,2246122574,13025721601,76194378042,449155863868,
%U A000087 2666126033850,15925105028685,95664343622234,577651490729530
%N A000087 Number of rooted planar maps.
%C A000087 The number of unrooted non-separable n-edge maps in the plane (planar 
               with a distinguished outside face). - Valery A. Liskovets (liskov(AT)im.bas-net.by), 
               Mar 17 2005
%D A000087 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000087 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000087 W. G. Brown, Enumeration of non-separable planar maps, Canad. J. Math., 
               15 (1963), 526-545.
%D A000087 V. A. Liskovets and T. R. Walsh, Enumeration of unrooted maps on the 
               plane, Rapport technique, UQAM, No. 2005-01, Montreal, Canada, 2005.
%H A000087 T. D. Noe, <a href="b000087.txt">Table of n, a(n) for n=1..200</a>
%H A000087 V. A. Liskovets and T. R. Walsh, <a href="http://dx.doi:10.1016/j.aam.2005.03.006">
               Counting unrooted maps on the plane</a>, Advances in Applied Math., 
               36, No.4 (2006), 364-387.
%F A000087 a(n)=(1/3n)[(n+2)binomial(3n, n)/((3n-2)(3n-1)) + Sum_{0<k<n, k|n}phi(n/
               k)binomial(3k, k)]+q(n) where phi is the Euler function A000010, 
               q(n)=0 if n is even and q(n)=2(n+1)binomial(3(n+1)/2, (n+1)/2)/(3(3n-1)(3n+1)) 
               if n is odd. - Valery A. Liskovets (liskov(AT)im.bas-net.by), Mar 
               17 2005
%Y A000087 Cf. A103938.
%Y A000087 Sequence in context: A146307 A063894 A024500 this_sequence A145667 A095067 
               A032259
%Y A000087 Adjacent sequences: A000084 A000085 A000086 this_sequence A000088 A000089 
               A000090
%K A000087 nonn
%O A000087 1,1
%A A000087 N. J. A. Sloane (njas(AT)research.att.com).
%E A000087 More terms from T. D. Noe (noe(AT)sspectra.com), Mar 14 2007

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