A022132 Fibonacci sequence beginning 4, 13.

4, 13, 17, 30, 47, 77, 124, 201, 325, 526, 851, 1377, 2228, 3605, 5833, 9438, 15271, 24709, 39980, 64689, 104669, 169358, 274027, 443385, 717412, 1160797, 1878209, 3039006, 4917215, 7956221, 12873436, 20829657, 33703093, 54532750, 88235843, 142768593

Offset

0,1

Links

Table of n, a(n) for n=0..35.

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+9*x)/(1-x-x^2).

a(n) = term (1,1) in the 1x2 matrix [4,9] . [1,1; 1,0]^n. (End)

a(n) = Lucas(n+4) + Fibonacci(n-4). - Greg Dresden and Kyle Wood, Mar 03 2022

Maple

a:= n -> (Matrix([[4, 9]]).Matrix([[1, 1], [1, 0]])^n)[1, 1]:
seq(a(n), n=0..35);  # Alois P. Heinz, Jul 31 2008

Mathematica

LinearRecurrence[{1, 1}, {4, 13}, 40] (* Harvey P. Dale, Jul 04 2017 *)

Crossrefs

Cf. A000032, A000045.

Sequence in context: A246145 A107462 A190863 * A041559 A339272 A280385

Adjacent sequences: A022129 A022130 A022131 * A022133 A022134 A022135

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved