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A002062
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n-th Fibonacci number + n.
(Formerly M0646 N0240)
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6
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0, 2, 3, 5, 7, 10, 14, 20, 29, 43, 65, 100, 156, 246, 391, 625, 1003, 1614, 2602, 4200, 6785, 10967, 17733, 28680, 46392, 75050, 121419, 196445, 317839, 514258, 832070, 1346300, 2178341, 3524611, 5702921, 9227500, 14930388, 24157854, 39088207, 63246025
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
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REFERENCES
| R. Honsberger, Ingenuity in Math., Random House, 1970, p. 96.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..500
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.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
| 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) ]
a(n)=2a(n-1)-a(n-3)-1 [From Kieren MacMillan (kieren(AT)alumni.rice.edu), Nov 08 2008]
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MAPLE
| A002062:=z*(-2+3*z)/(z**2+z-1)/(z-1)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]
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
(Mupad) numlib::fibonacci(n)+n $ n = 0..48; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 08 2008
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MATHEMATICA
| lst={}; Do[f=Fibonacci[n]+n; AppendTo[lst, f], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 20 2009]
Table[Fibonacci[n]+n, {n, 0, 30}] (* From Harvey P. Dale, Jul 27 2011 *)
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CROSSREFS
| Sequence in context: A123975 A094984 A107332 * A005688 A120446 A082531
Adjacent sequences: A002059 A002060 A002061 * A002063 A002064 A002065
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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