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A081075 a(n) = Fibonacci(4n+2) - 3. 0
5, 52, 374, 2581, 17708, 121390, 832037, 5702884, 39088166, 267914293, 1836311900, 12586269022, 86267571269, 591286729876, 4052739537878, 27777890035285, 190392490709132, 1304969544928654, 8944394323791461 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

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

LINKS

Table of n, a(n) for n=1..19.

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) = -3 + 4*((7/2 - (3/2)*sqrt(5))^n + (7/2 + (3/2)*sqrt(5))^n) + (9/5)*sqrt(5) ((7/2 + (3/2)*sqrt(5))^n - (7/2 - (3/2)*sqrt(5))^n). - Paolo P. Lava, Dec 01 2008

G.f.: x*(2*x^2-12*x-5)/((x-1)*(x^2-7*x+1)). - Colin Barker, Jun 22 2012

a(n) = Fibonacci(2*n+3)*Lucas(2*n-1). - Ehren Metcalfe, Apr 21 2019

MAPLE

with(combinat): for n from 1 to 40 do printf(`%d, `, fibonacci(4*n+2)-3) od: # James A. Sellers, Mar 05 2003

MATHEMATICA

Array[Fibonacci[4 # + 2] - 3 &, 19] (* Michael De Vlieger, Apr 21 2019 *)

PROG

(MAGMA) [Fibonacci(4*n+2)-3: n in [1..50]]; // Vincenzo Librandi, Apr 20 2011

CROSSREFS

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

Sequence in context: A045539 A281202 A173719 * A247766 A247777 A193809

Adjacent sequences:  A081072 A081073 A081074 * A081076 A081077 A081078

KEYWORD

nonn,easy

AUTHOR

R. K. Guy, Mar 04 2003

EXTENSIONS

More terms from James A. Sellers, Mar 05 2003

STATUS

approved

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Last modified May 16 14:39 EDT 2021. Contains 343949 sequences. (Running on oeis4.)