Search: id:A006493
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%I A006493 M4063
%S A006493 1,0,6,7,28,54,135,286,627,1313,2730,5565,11212,22304,43911,85614,
%T A006493 165490,317373,604296,1143054,2149074,4017950,7473180,13832910,25490115,
               46774448
%N A006493 Generalized Lucas numbers.
%D A006493 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006493 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.
%D A006493 L. Carlitz and R. Scoville, Zero-one sequences and Fibonacci numbers, 
               Fib. Quart., 15 (1977), 246-254.
%H A006493 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 A006493 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 A006493 G.f. has denominator (1-x-x^2)^5.
%p A006493 A006493:=(1-2*z+2*z**2)*(z-1)**3/(z**2+z-1)**5; [Conjectured by S. Plouffe 
               in his 1992 dissertation.]
%p A006493 a:= n-> (Matrix([[7,6,0,1,0$4,-2,18]]). Matrix(10, (i,j)-> if (i=j-1) 
               then 1 elif j=1 then [5,-5,-10,15,11, -15,-10,5,5,1][i] else 0 fi)^n)[1,
               7]: seq (a(n), n=3..28); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Aug 26 2008]
%Y A006493 Sequence in context: A042419 A037956 A095369 this_sequence A037375 A159582 
               A041553
%Y A006493 Adjacent sequences: A006490 A006491 A006492 this_sequence A006494 A006495 
               A006496
%K A006493 nonn
%O A006493 3,3
%A A006493 N. J. A. Sloane (njas(AT)research.att.com).

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