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A022133 Fibonacci sequence beginning 4, 15. 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Feb 14 2016 *)

CROSSREFS

Sequence in context: A032826 A190709 A166732 * A212921 A225562 A100783

Adjacent sequences:  A022130 A022131 A022132 * A022134 A022135 A022136

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 20 16:53 EDT 2017. Contains 289628 sequences.