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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000032, A000045.

Programs

Magma

[10*Fibonacci(n): n in [0..40]]; // Vincenzo Librandi, Dec 31 2016

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 *)

SageMath

A022093=BinaryRecurrenceSequence(1,1,0,10)
[A022093(n) for n in range(51)] # G. C. Greubel, Jun 02 2025

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