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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000045.

Programs

Mathematica

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

PARI

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

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)