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A022093 Fibonacci sequence beginning 0, 10. 1
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 (list; graph; refs; listen; history; text; internal format)
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

MATHEMATICA

a={}; b=0; c=10; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 4!}]; a (* Vladimir Joseph Stephan Orlovsky, Sep 17 2008 *)

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

CROSSREFS

Cf. A000045.

Sequence in context: A205724 A040091 A168461 * A076817 A200984 A185993

Adjacent sequences:  A022090 A022091 A022092 * A022094 A022095 A022096

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified April 29 17:16 EDT 2017. Contains 285607 sequences.