0,2

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

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).

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.

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]

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

lst={}; Do[f=Fibonacci[n]+n; AppendTo[lst, f], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 20 2009]

Sequence in context: A123975 A094984 A107332 this_sequence A005688 A120446 A082531

Adjacent sequences: A002059 A002060 A002061 this_sequence A002063 A002064 A002065

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).