A022133 Fibonacci sequence beginning 4, 15.

4, 15, 19, 34, 53, 87, 140, 227, 367, 594, 961, 1555, 2516, 4071, 6587, 10658, 17245, 27903, 45148, 73051, 118199, 191250, 309449, 500699, 810148, 1310847, 2120995, 3431842, 5552837, 8984679, 14537516

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+11*x)/(1-x-x^2).

a(n) = term (1,1) in the 1 X 2 matrix [4,11] . [1,1; 1,0]^n. (End)

Maple

a:= n-> (Matrix([[4, 11]]).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=15; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 40, 1}]; a (* Vladimir Joseph Stephan Orlovsky, Jul 23 2008 *)
Transpose[NestList[{#[[2]], #[[2]]+#[[1]]}&, {4, 15}, 40]][[1]] (* Harvey P. Dale, Dec 12 2010 *)
LinearRecurrence[{1, 1}, {4, 15}, 40] (* Jean-François Alcover, Feb 14 2016 *)

Prog

(PARI) a(n)=([0, 1; 1, 1]^n*[4; 15])[1, 1] \\ Charles R Greathouse IV, Jun 01 2026

Crossrefs

Sequence in context: A032826 A190709 A166732 * A383360 A212921 A359958

Adjacent sequences: A022130 A022131 A022132 * A022134 A022135 A022136

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved