A022122 Fibonacci sequence beginning 3, 10.

3, 10, 13, 23, 36, 59, 95, 154, 249, 403, 652, 1055, 1707, 2762, 4469, 7231, 11700, 18931, 30631, 49562, 80193, 129755, 209948, 339703, 549651, 889354, 1439005, 2328359, 3767364, 6095723, 9863087, 15958810, 25821897, 41780707, 67602604, 109383311, 176985915

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

Mathematica

a={};b=3;c=10;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 *)

Formula

G.f.: (3+7x)/(1-x-x^2). - Philippe Deléham, Nov 19 2008

From Wajdi Maaloul, Jun 09 2022: (Start)

a(n) = 3*Lucas(n+1) + Fibonacci(n).

a(n) = 3*Fibonacci(n+1) + 7*Fibonacci(n).

a(n) = a(n-1) + a(n-2). (End)