Search: id:A001911
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%I A001911 M2546 N1007
%S A001911 0,1,3,6,11,19,32,53,87,142,231,375,608,985,1595,2582,4179,6763,10944,
%T A001911 17709,28655,46366,75023,121391,196416,317809,514227,832038,1346267,
%U A001911 2178307,3524576,5702885,9227463,14930350,24157815,39088167,63245984
%N A001911 Fibonacci numbers - 2.
%D A001911 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001911 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001911 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 A001911 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               233.
%D A001911 D. G. Rogers, An application of renewal sequences to the dimer problem, 
               pp. 142-153 of Combinatorial Mathematics VI (Armidale 1978), Lect. 
               Notes Math. 748, 1979.
%H A001911 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 A001911 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.
%H A001911 D. J. Broadhurst, <a href="http://arXiv.org/abs/hep-th/9604128">On the 
               enumeration of irreducible k-fold Euler sums and their roles in knot 
               theory and field theory</a>
%F A001911 a(n) = a(n-1) + a(n-2) + 2, a(0)=0, a(1)=1.
%F A001911 G.f.: (x+x^2)/(1-2*x+x^3).
%F A001911 Sum of consecutive pairs of partial sums of Fibonacci numbers. - Paul 
               Barry (pbarry(AT)wit.ie), Apr 17 2004
%F A001911 a(n) = A101220(2, 1, n) - Ross La Haye (rlahaye(AT)new.rr.com), Jan 28 
               2005
%F A001911 a(n) = A108617(n+1, 2) = A108617(n+1, n-1) for n>0; - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Jun 12 2005
%F A001911 a(n) = term (1,1) in the 1x3 matrix [0,-1,1].[1,1,0; 1,0,0; 2,0,1]^n. 
               - Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 24 2008
%p A001911 a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=a[n-1]+a[n-2]+2 od: seq(a[n],
               n=0..50); (Miklos Kristof (kristmikl(AT)freemail.hu), Mar 09 2005)
%p A001911 with(combinat):a:=n->sum(fibonacci(j),j=2..n): seq(a(n),n=1..37); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Oct 03 2007
%p A001911 A001911:=(1+z)/(z-1)/(z**2+z-1); [Conjectured by S. Plouffe in his 1992 
               dissertation.]
%p A001911 a := n -> (Matrix([[0,-1,1]]) . Matrix([[1,1,0], [1,0,0], [2,0,1]])^n)[1,
               1]; seq (a(n), n=0..50); - Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Jul 24 2008
%Y A001911 a(n) = A000045(n+3)-2.
%Y A001911 Partial sums of F(n+1)=A000045(n+1).
%Y A001911 Cf. A000071.
%Y A001911 Right-hand column 3 of triangle A011794.
%Y A001911 Sequence in context: A001976 A144115 A116557 this_sequence A020957 A116365 
               A055417
%Y A001911 Adjacent sequences: A001908 A001909 A001910 this_sequence A001912 A001913 
               A001914
%K A001911 nonn,easy,nice
%O A001911 0,3
%A A001911 N. J. A. Sloane (njas(AT)research.att.com).
%E A001911 More terms and better description from Michael Somos

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