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A081006 Fibonacci(4n)-1, or Fibonacci(2n+1)*Lucas(2n-1). 1
2, 20, 143, 986, 6764, 46367, 317810, 2178308, 14930351, 102334154, 701408732, 4807526975, 32951280098, 225851433716, 1548008755919, 10610209857722, 72723460248140, 498454011879263, 3416454622906706, 23416728348467684, 160500643816367087 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Apart from the offset, the same as A003481. - R. J. Mathar, Sep 18 2008

REFERENCES

Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..500

Index entries for linear recurrences with constant coefficients, signature (8,-8,1).

FORMULA

a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3).

a(n) = -1+(3/2)*{[(7/2)-(3/2)*sqrt(5)]^n+[(7/2)+(3/2)*sqrt(5)]^n}+(7/10)*sqrt(5)*{[(7/2)+(3 /2)*sqrt(5)]^n-[(7/2)-(3/2)*sqrt(5)]^n}, with n>=0. - Paolo P. Lava, Dec 01 2008

G.f.: x*(x^2-4*x-2)/((x-1)*(x^2-7*x+1)). - Colin Barker, Jun 24 2012

MAPLE

with(combinat) for n from 0 to 25 do printf(`%d, `, fibonacci(4*n)-1) od # James A. Sellers, Mar 03 2003

MATHEMATICA

Fibonacci[4*Range[30]]-1 (* or *) LinearRecurrence[{8, -8, 1}, {2, 20, 143}, 30] (* Harvey P. Dale, Mar 19 2018 *)

PROG

(MAGMA) [Fibonacci(4*n)-1: n in [1..100]]; // Vincenzo Librandi, Apr 15 2011

CROSSREFS

Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers).

Sequence in context: A279112 A229454 A003490 * A003481 A000183 A198052

Adjacent sequences:  A081003 A081004 A081005 * A081007 A081008 A081009

KEYWORD

nonn,easy

AUTHOR

R. K. Guy, Mar 01 2003

EXTENSIONS

More terms from James A. Sellers, Mar 03 2003

STATUS

approved

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Last modified August 19 21:29 EDT 2018. Contains 313896 sequences. (Running on oeis4.)