A022093 Fibonacci sequence beginning 0, 10.

0, 10, 10, 20, 30, 50, 80, 130, 210, 340, 550, 890, 1440, 2330, 3770, 6100, 9870, 15970, 25840, 41810, 67650, 109460, 177110, 286570, 463680, 750250, 1213930, 1964180, 3178110, 5142290, 8320400, 13462690, 21783090, 35245780, 57028870, 92274650, 149303520, 241578170

Offset

0,2

References

A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, p. 15.

Links

Vincenzo Librandi, 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

a(n) = 10*F(n) = F(n+4) + F(n+2) + F(n-2) + F(n-4) for n>3, where F = A000045.

a(n) = round((4*phi-2)*phi^n) for n>4. - Thomas Baruchel, Sep 08 2004

G.f.: 10*x/(1 - x - x^2). - Philippe Deléham, Nov 20 2008

a(n) = F(n+5) + F(n-5) - 5*F(n) for n>0. - Bruno Berselli, Dec 29 2016

a(n) = Lucas(n+3) + Lucas(n-3), where Lucas(-n) = (-1)^n*Lucas(n) for the negative indices. - Bruno Berselli, Jun 13 2017

E.g.f.: 20*exp(x/2)*sinh(sqrt(5)*x/2)/sqrt(5). - Stefano Spezia, Nov 09 2025

Mathematica

LinearRecurrence[{1, 1}, {0, 10}, 40] (* Bruno Berselli, Dec 30 2016 *)
Table[Fibonacci[n + 5] + Fibonacci[n - 5] - 5 Fibonacci[n], {n, 1, 40}] (* Bruno Berselli, Dec 30 2016 *)
Table[10 Fibonacci[n], {n, 0, 100}] (* Vincenzo Librandi, Dec 31 2016 *)

Prog

(Magma) [10*Fibonacci(n): n in [0..40]]; // Vincenzo Librandi, Dec 31 2016
(SageMath)
A022093=BinaryRecurrenceSequence(1, 1, 0, 10)
[A022093(n) for n in range(51)] # G. C. Greubel, Jun 02 2025

Crossrefs

Cf. A000032, A000045.

Sequence in context: A168461 A309464 A368362 * A332874 A076817 A324494

Adjacent sequences: A022090 A022091 A022092 * A022094 A022095 A022096

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved