Search: id:A002062
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%I A002062 M0646 N0240
%S A002062 0,2,3,5,7,10,14,20,29,43,65,100,156,246,391,625,1003,1614,2602,
%T A002062 4200,6785,10967,17733,28680,46392,75050,121419,196445,317839,514258
%N A002062 n-th Fibonacci number + n.
%C A002062 Let _x indicate the sequence offset. Then a(n+2)_0 = A006355(n+4)_0 - 
               A066982(n+1)_1 (conjecture); (a(n)) = em[K* ]seq( .25'i - .25'j - 
               .25'k - .25i' + .25j' - .75k' - .25'ii' - .25'jj' - .25'kk' - .25'ij' 
               - .25'ik' - .75'ji' + .25'jk' - .25'ki' - .75'kj' + .75e), apart 
               from initial term. - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), 
               Nov 19 2004
%D A002062 R. Honsberger, Ingenuity in Math., Random House, 1970, p. 96.
%D A002062 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002062 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A002062 T. D. Noe, <a href="b002062.txt">Table of n, a(n) for n=0..500</a>
%H A002062 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 A002062 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 A002062 Convolution of natural numbers n >= 1 with Fibonacci numbers F(k), k 
               >= -3, (F(-k)=(-1)^(k+1)*F(k)); G.f.: x*(2-3*x)/((1-x-x^2)*(1-x)^2) 
               [ Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) ]
%F A002062 a(n)=2a(n-1)-a(n-3)-1 [From Kieren MacMillan (kieren(AT)alumni.rice.edu), 
               Nov 08 2008]
%p A002062 A002062:=z*(-2+3*z)/(z**2+z-1)/(z-1)**2; [Conjectured by S. Plouffe in 
               his 1992 dissertation.]
%p A002062 a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=a[n-1]+a[n-2] od: seq(a[n]+n, 
               n=0..29); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 20 
               2008
%p A002062 (Mupad) numlib::fibonacci(n)+n $ n = 0..48; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               May 08 2008
%t A002062 lst={};Do[f=Fibonacci[n]+n;AppendTo[lst,f],{n,0,5!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Mar 20 2009]
%Y A002062 Sequence in context: A123975 A094984 A107332 this_sequence A005688 A120446 
               A082531
%Y A002062 Adjacent sequences: A002059 A002060 A002061 this_sequence A002063 A002064 
               A002065
%K A002062 nonn,easy,nice
%O A002062 0,2
%A A002062 N. J. A. Sloane (njas(AT)research.att.com).

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