A022134 Fibonacci sequence beginning 4, 17.

4, 17, 21, 38, 59, 97, 156, 253, 409, 662, 1071, 1733, 2804, 4537, 7341, 11878, 19219, 31097, 50316, 81413, 131729, 213142, 344871, 558013, 902884, 1460897, 2363781, 3824678, 6188459, 10013137, 16201596

Offset

0,1

Links

Table of n, a(n) for n=0..30.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (1, 1).

Formula

From Alois P. Heinz, Jul 31 2008: (Start)

G.f.: (4+13*x)/(1-x-x^2).

a(n) = term (1,1) in the 1x2 matrix [4,13] . [1,1; 1,0]^n. (End)

Maple

a:= n -> (Matrix([[4, 13]]).Matrix([[1, 1], [1, 0]])^n)[1, 1]:
seq(a(n), n=0..35);  # Alois P. Heinz, Jul 31 2008

Mathematica

a={}; b=4; c=17; 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}, {4, 17}, 40] (* Harvey P. Dale, Sep 05 2015 *)

Crossrefs

Sequence in context: A212748 A032828 A193379 * A041529 A042033 A372749

Adjacent sequences: A022131 A022132 A022133 * A022135 A022136 A022137

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved