login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A081012 a(n) = Fibonacci(4n+1) - 2, or Fibonacci(2n+2)*Lucas(2n-1). 1
3, 32, 231, 1595, 10944, 75023, 514227, 3524576, 24157815, 165580139, 1134903168, 7778742047, 53316291171, 365435296160, 2504730781959, 17167680177563, 117669030460992, 806515533049391, 5527939700884755, 37889062373143904 (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

G. C. Greubel, Table of n, a(n) for n = 1..1000

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) = -2 + (5/2)*{[(7/2)-(3/2)*sqrt(5)]^n + [(7/2)+(3/2)*sqrt(5)]^n + (11/10)*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*(3+8*x-x^2)/((1-x)*(1-7*x+x^2)). - Colin Barker, Jun 22 2012

a(n) = 7*a(n-1) - a(n-2) + 10, n>=3. - R. J. Mathar, Nov 07 2015

MAPLE

with(combinat) for n from 0 to 25 do printf(`%d, `, fibonacci(4*n+1)-2) od # James A. Sellers, Mar 03 2003

MATHEMATICA

Fibonacci[4*Range[30]+1] -2 (* G. C. Greubel, Jul 14 2019 *)

PROG

(MAGMA) [Fibonacci(4*n+1)-2: n in [1..30]]; // Vincenzo Librandi, Apr 20 2011

(PARI) vector(30, n, fibonacci(4*n+1)-2) \\ G. C. Greubel, Jul 14 2019

(Sage) [fibonacci(4*n+1)-2 for n in (1..30)] # G. C. Greubel, Jul 14 2019

(GAP) List([1..30], n-> Fibonacci(4*n+1) -2); # G. C. Greubel, Jul 14 2019

CROSSREFS

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

Sequence in context: A264574 A002059 A028447 * A187919 A198320 A035533

Adjacent sequences:  A081009 A081010 A081011 * A081013 A081014 A081015

KEYWORD

nonn,easy

AUTHOR

R. K. Guy, Mar 01 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 15 21:37 EST 2019. Contains 329168 sequences. (Running on oeis4.)