%I A006566 M5089
%S A006566 0,1,20,84,220,455,816,1330,2024,2925,4060,5456,7140,9139,11480,14190,
%T A006566 17296,20825,24804,29260,34220,39711,45760,52394,59640,67525,76076,
%U A006566 85320,95284,105995,117480,129766,142880,156849,171700,187460,204156
%N A006566 Dodecahedral numbers: n(3n-1)(3n-2)/2.
%C A006566 Schlaefli symbol for this polyhedron: {5,3}
%C A006566 A093485 = first differences; A124388 = second differences; third differences 
               = 27. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 
               30 2006
%D A006566 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006566 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 A006566 T. D. Noe, <a href="b006566.txt">Table of n, a(n) for n=0..1000</a>
%H A006566 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 A006566 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.
%H A006566 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A006566 Hyun Kwang Kim, <a href="http://com2mac.postech.ac.kr/papers/2001/01-22.pdf">
               On Regular Polytope Numbers</a>
%F A006566 G.f.: x(1+16x+10x^2)/(1-x)^4. a(n) = A000292(3n-3) = A054776(n)/6 = n*A060544(n).
%F A006566 a(n) = C(n+2,3) + 16 C(n+1,3) + 10 C(n,3)
%p A006566 A006566:=(1+16*z+10*z**2)/(z-1)**4; [Conjectured by S. Plouffe in his 
               1992 dissertation.]
%o A006566 (PARI) a(n)=n*(3*n-1)*(3*n-2)/2
%Y A006566 Sequence in context: A156389 A044207 A044588 this_sequence A154077 A027849 
               A071092
%Y A006566 Adjacent sequences: A006563 A006564 A006565 this_sequence A006567 A006568 
               A006569
%K A006566 nonn,easy,nice
%O A006566 0,3
%A A006566 N. J. A. Sloane (njas(AT)research.att.com).
%E A006566 More terms from Henry Bottomley (se16(AT)btinternet.com), Nov 23 2001