%I A006565 M4942
%S A006565 0,1,14,130,700,2635,7826,19684,43800,88725,166870,295526,498004,
%T A006565 804895,1255450,1899080,2796976,4023849,5669790,7842250,10668140,
%U A006565 14296051,18898594,24674860,31853000,40692925,51489126,64573614
%N A006565 Number of ways to color vertices of a hexagon using <= n colors, allowing 
               only rotations.
%D A006565 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006565 S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques 
               Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A006565 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A006565 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%F A006565 (n^6 + n^3 + 2n^2 + 2n)/6.
%p A006565 A006565 := n-> (n^6+n^3+2*n^2+2*n)/6.
%p A006565 A006565:=-(1+7*z+53*z**2+49*z**3+10*z**4)/(z-1)**7; [Conjectured by S. 
               Plouffe in his 1992 dissertation.]
%Y A006565 Cf. A027670.
%Y A006565 Sequence in context: A166794 A038841 A021354 this_sequence A026936 A021114 
               A113976
%Y A006565 Adjacent sequences: A006562 A006563 A006564 this_sequence A006566 A006567 
               A006568
%K A006565 nonn
%O A006565 0,3
%A A006565 N. J. A. Sloane (njas(AT)research.att.com).