Search: id:A006564
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%I A006564 M4837
%S A006564 1,12,48,124,255,456,742,1128,1629,2260,3036,3972,5083,6384,7890,9616,
%T A006564 11577,13788,16264,19020,22071,25432,29118,33144,37525,42276,47412,52948,
               58899
%N A006564 Icosahedral numbers: n(5n^2 -5n + 2)/2.
%C A006564 Schlaefli symbol for this polyhedron: {3,5}
%D A006564 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006564 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 A006564 T. D. Noe, <a href="b006564.txt">Table of n, a(n) for n=1..1000</a>
%H A006564 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 A006564 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 A006564 Hyun Kwang Kim, <a href="http://com2mac.postech.ac.kr/papers/2001/01-22.pdf">
               On Regular Polytope Numbers</a>
%F A006564 a(n) = C(n+2,3) + 8 C(n+1,3) + 6 C(n,3)
%p A006564 A006564:=(1+8*z+6*z**2)/(z-1)**4; [Conjectured by S. Plouffe in his 1992 
               dissertation.]
%Y A006564 Cf. A000292, A000578, A005900, A006566
%Y A006564 Sequence in context: A009958 A135453 A165280 this_sequence A059162 A117027 
               A161171
%Y A006564 Adjacent sequences: A006561 A006562 A006563 this_sequence A006565 A006566 
               A006567
%K A006564 nonn,nice,easy
%O A006564 1,2
%A A006564 N. J. A. Sloane (njas(AT)research.att.com).

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