A022355 Fibonacci sequence beginning 0, 21.

0, 21, 21, 42, 63, 105, 168, 273, 441, 714, 1155, 1869, 3024, 4893, 7917, 12810, 20727, 33537, 54264, 87801, 142065, 229866, 371931, 601797, 973728, 1575525, 2549253, 4124778, 6674031, 10798809, 17472840, 28271649, 45744489, 74016138, 119760627, 193776765

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Tanya Khovanova, Recursive Sequences

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

Formula

G.f.: 21*x/(1 - x - x^2). - Philippe Deléham, Nov 20 2008

a(n) = 21*Fibonacci(n) = h*Fibonacci(n+k) + Fibonacci(n+k-h) with h=8, k=2. - Bruno Berselli, Feb 20 2017

From Colin Barker, Feb 20 2017: (Start)

a(n) = -21*(((1-sqrt(5))/2)^n - ((1+sqrt(5))/2)^n) / sqrt(5).

a(n) = a(n-1) + a(n-2) for n>1.

(End)

Mathematica

LinearRecurrence[{1, 1}, {0, 21}, 30] (* Harvey P. Dale, Dec 13 2014 *)

Prog

(PARI) concat(0, Vec(21*x/(1 - x - x^2) + O(x^50))) \\ Colin Barker, Feb 20 2017

Crossrefs

Cf. A000045.

Sequence in context: A158772 A151910 A040421 * A371100 A048245 A246034

Adjacent sequences: A022352 A022353 A022354 * A022356 A022357 A022358

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved