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 A002062 a(n) = n-th Fibonacci number + n. (Formerly M0646 N0240) 13
 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; text; internal format)
 OFFSET 0,2 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, Nov 19 2004 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). LINKS T. D. Noe, Table of n, a(n) for n = 0..500 Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992. Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992. Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,1). FORMULA G.f.: x*(-2+3*x) ) / ( (x^2+x-1)*(x-1)^2 ). - Simon Plouffe in his 1992 dissertation 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 a(n) = 2*a(n-1)-a(n-3)-1. - Kieren MacMillan, Nov 08 2008 a(n) = 3*a(n-1)-2*a(n-2)-a(n-3)+a(n-4). - Emmanuel Vantieghem, May 19 2016 E.g.f.: 2*exp(x/2)*sinh(sqrt(5)*x/2)/sqrt(5) + x*exp(x). - Ilya Gutkovskiy, Apr 11 2017 MAPLE 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, Mar 20 2008 MATHEMATICA lst={}; Do[f=Fibonacci[n]+n; AppendTo[lst, f], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 20 2009 *) Table[Fibonacci[n]+n, {n, 0, 30}] (* Harvey P. Dale, Jul 27 2011 *) PROG (MuPAD) numlib::fibonacci(n)+n \$ n = 0..48; // Zerinvary Lajos, May 08 2008 (Haskell) a002062 n = a000045 n + toInteger n a002062_list = 0 : 2 : 3 : (map (subtract 1) \$    zipWith (-) (map (* 2) \$ drop 2 a002062_list) a002062_list) -- Reinhard Zumkeller, Oct 03 2012 (PARI) a(n)=fibonacci(n) + n \\ Charles R Greathouse IV, Oct 03 2016 CROSSREFS Cf. A001611, A160536, A212272. Sequence in context: A214077 A094984 A107332 * A005688 A241550 A221943 Adjacent sequences:  A002059 A002060 A002061 * A002063 A002064 A002065 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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Last modified March 23 12:32 EDT 2018. Contains 301123 sequences. (Running on oeis4.)