A097657 Fibonacci sequence with first two terms 11 and 23.

11, 23, 34, 57, 91, 148, 239, 387, 626, 1013, 1639, 2652, 4291, 6943, 11234, 18177, 29411, 47588, 76999, 124587, 201586, 326173, 527759, 853932, 1381691, 2235623, 3617314, 5852937, 9470251, 15323188, 24793439

Offset: 0

Author

Parthasarathy Nambi, Sep 20 2004

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000045.

Programs

Mathematica

a[0] := 11; a[1] := 23; a[n_] := a[n - 1] + a[n - 2]; Table[a[n], {n, 0, 25}] (* Stefan Steinerberger, Mar 06 2006 *)

PARI

a(n)=([0,1; 1,1]^n*[11;23])[1,1] \\ Charles R Greathouse IV, Feb 20 2017

Formula

a(n) = a(n-1) + a(n-2) for n > 1, a(0) = 11, a(1) = 23.

G.f.: (11 + 12*x)/(1 - x - x^2). - Philippe Deléham, Nov 20 2008

a(n) = h*Fibonacci(n+k) + Fibonacci(n+k-h) with h=7, k=3. - Bruno Berselli, Feb 20 2017

Extensions

More terms from Stefan Steinerberger, Mar 06 2006