Search: id:A006060
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%I A006060 M5425
%S A006060 1,253,49141,9533161,1849384153,358770992581,69599723176621,
%T A006060 13501987525271953,2619315980179582321,508133798167313698381,
%U A006060 98575337528478677903653,19123107346726696199610361
%N A006060 Triangular star numbers.
%D A006060 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006060 M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, 
               NY, 1988, p. 20.
%H A006060 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 A006060 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 A006060 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               StarNumber.html">Star Number</a>
%F A006060 G.f.: [1+58x+x^2]/[(x-1)(1-194x+x^2)]. - Ralf Stephan, Apr 23 2004
%p A006060 A006060:=-(1+58*z+z**2)/(z-1)/(z**2-194*z+1); [Conjectured (correctly) 
               by S. Plouffe in his 1992 dissertation.]
%p A006060 a := n -> (Matrix([[253,1,1]]). Matrix([[195,1,0], [ -195,0,1], [1,0,
               0]])^n)[1,3]; seq (a(n), n=1..20); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Aug 14 2008]
%Y A006060 Cf. A000567, A003154, A006061, A051673.
%Y A006060 Sequence in context: A070193 A054737 A123013 this_sequence A077695 A145628 
               A144855
%Y A006060 Adjacent sequences: A006057 A006058 A006059 this_sequence A006061 A006062 
               A006063
%K A006060 nonn
%O A006060 1,2
%A A006060 N. J. A. Sloane (njas(AT)research.att.com).
%E A006060 Extended by Eric Weisstein (eric(AT)weisstein.com), Mar 01, 2002

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