%I A006079 M3515
%S A006079 1,1,0,1,4,16,56,197,680,2368,8272,29162,103544,370592,1335504,
%T A006079 4844205,17672400,64810240,238795040,883585406,3281967832,
%U A006079 12232957152,45740929104,171529130786,644950721584,2430970600576
%N A006079 Number of asymmetric planted projective plane trees with n+1 nodes; bracelets 
               (reversible necklaces) with n black beads and n-1 white beads.
%C A006079 "DHK[ n ](2n-1)" (bracelet, identity, unlabeled, n parts, evaluated at 
               2n) transform of 1,1,1,1...
%D A006079 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006079 P. K. Stockmeyer, The charm bracelet problem and its applications, pp. 
               339-349 of Graphs and Combinatorics (Washington, Jun 1973), Ed. by 
               R. A. Bari and F. Harary. Lect. Notes Math., Vol. 406. Springer-Verlag, 
               1974.
%H A006079 T. D. Noe, <a href="b006079.txt">Table of n, a(n) for n=1..200</a>
%H A006079 C. G. Bower, <a href="transforms2.html">Transforms (2)</a>
%H A006079 <a href="Sindx_Br.html#bracelets">Index entries for sequences related 
               to bracelets</a>
%H A006079 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%H A006079 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%F A006079 Let c(x) = (1-sqrt(1-4*x))/(2*x) = g.f. for Catalans (A000108), let d(x) 
               = x/(1-x-x^2*c(x^2)) = g.f. for A001405. Then g.f. for the asymmetric 
               planted projective plane trees sequence is (x*c(x)-d(x))/2 (the initial 
               terms from this version are slightly different).
%F A006079 a(n+1) = (CatalanNumber(n)-binomial(n,Floor[n/2]))/2 (for n>=3). - David 
               Callan (callan(AT)stat.wisc.edu), Jul 14 2006
%e A006079 For the asymmetric planted projective plane trees sequence we have a(5) 
               = 4, a(6) = 16, a(7) = 56, ...
%Y A006079 Cf. A000029, A000031, A006080-A006082.
%Y A006079 Sequence in context: A025182 A057585 A097128 this_sequence A122032 A034514 
               A126644
%Y A006079 Adjacent sequences: A006076 A006077 A006078 this_sequence A006080 A006081 
               A006082
%K A006079 nonn,nice,easy
%O A006079 1,5
%A A006079 N. J. A. Sloane (njas(AT)research.att.com).
%E A006079 Alternative description and more terms from Christian G. Bower (bowerc(AT)usa.net).