A022123 Fibonacci sequence beginning 3, 11.

3, 11, 14, 25, 39, 64, 103, 167, 270, 437, 707, 1144, 1851, 2995, 4846, 7841, 12687, 20528, 33215, 53743, 86958, 140701, 227659, 368360, 596019, 964379, 1560398, 2524777, 4085175, 6609952, 10695127, 17305079, 28000206, 45305285, 73305491, 118610776

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (1,1).

Crossrefs

Cf. A000032, A000045.

Programs

Magma

[8*Fibonacci(n) + 3*Fibonacci(n+1): n in [0..40]]; // Vincenzo Librandi, Mar 17 2020

Mathematica

a={};b=3;c=11;AppendTo[a, b];AppendTo[a, c];Do[b=b+c;AppendTo[a, b];c=b+c;AppendTo[a, c], {n, 4!}];a (* Vladimir Joseph Stephan Orlovsky, Sep 17 2008 *)
LinearRecurrence[{1,1},{3,11},40] (* Harvey P. Dale, Jan 27 2012 *)

Formula

G.f.: (3+8*x)/(1-x-x^2). - Philippe Deléham, Nov 19 2008

a(n) = 8*Fibonacci(n) + 3*Fibonacci(n+1). - Lechoslaw Ratajczak, Mar 14 2020

a(n) = a(n-1) + a(n-2). - Wesley Ivan Hurt, Jun 17 2021