0,3

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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.

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 233.

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.

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.

D. J. Broadhurst, On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory

a(n) = a(n-1) + a(n-2) + 2, a(0)=0, a(1)=1.

G.f.: (x+x^2)/(1-2*x+x^3).

Sum of consecutive pairs of partial sums of Fibonacci numbers. - Paul Barry (pbarry(AT)wit.ie), Apr 17 2004

a(n) = A101220(2, 1, n) - Ross La Haye (rlahaye(AT)new.rr.com), Jan 28 2005

a(n) = A108617(n+1, 2) = A108617(n+1, n-1) for n>0; - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 12 2005

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

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)

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

A001911:=(1+z)/(z-1)/(z**2+z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]

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

a(n) = A000045(n+3)-2.

Partial sums of F(n+1)=A000045(n+1).

Cf. A000071.

Right-hand column 3 of triangle A011794.

Sequence in context: A001976 A144115 A116557 this_sequence A020957 A116365 A055417

Adjacent sequences: A001908 A001909 A001910 this_sequence A001912 A001913 A001914

nonn,easy,nice

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

More terms and better description from Michael Somos