1,2

E. S. Egge and T. Mansour, Restricted permutations, Fibonacci numbers and k-generalized Fibonacci numbers.

Dan Sewell Ward, Modified Fibonacci Sequence.

a(0)=0, a(1)=1, a(n)=a(n-1)+a(n-2)+3.

a(n) = A000204(n+2)-3 = A000045(2n+4)/A000045(n+2) - 3. - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 05 2003

G.f.: x(1+2x)/[(1-x)*(1-x-x^2)]. Differences of A023537. - Ralf Stephan, Feb 07 2004

a(n) = A101220(3, 1, n) - Ross La Haye (rlahaye(AT)new.rr.com), Jan 28 2005

Sum of the first n Lucas numbers, that is, A000204(1) to A000204(n). - T. D. Noe (noe(AT)sspectra.com), Oct 10 2005

a(n)=F(n)+F(n+2)-3 n>=2 {where F(n) is the n-th Fibonacci number} - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2008

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=a[n-1]+a[n-2]+3 od: seq(a[n], n=1..50); (Miklos Kristof (kristmikl(AT)freemail.hu), Mar 09 2005)

with(combinat): seq(fibonacci(n)+fibonacci(n+2)-3, n=2..36); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2008

g:=(1+z^2)/(1-z-z^2): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)-3, n=3..37); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 09 2009]

T(n, n+1), T given by A027960.

Sequence in context: A011896 A024624 A098196 this_sequence A018921 A103536 A011970

Adjacent sequences: A027958 A027959 A027960 this_sequence A027962 A027963 A027964

nonn

Clark Kimberling (ck6(AT)evansville.edu)