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

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A097512 a(n) = 6*Lucas(2n) - Fib(2n+2). 1
11, 15, 34, 87, 227, 594, 1555, 4071, 10658, 27903, 73051, 191250, 500699, 1310847, 3431842, 8984679, 23522195, 61581906, 161223523, 422088663, 1105042466, 2893038735, 7574073739, 19829182482, 51913473707, 135911238639 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Sequence relates bisections of Lucas and Fibonacci numbers.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (3,-1).

FORMULA

a(n) = 8*Lucas(2n) - Lucas(2n+2) - 2*Fib(2n-1) = 8*A005248(n) - A005248(n+1) - 2*A001519(n).

a(n+1)/a(n) approaches the golden ratio phi + 1 = (3+sqrt(5))/2.

a(n) = 3*a(n-1)-a(n-2) with a(0)=11 and a(1)=15. G.f.: (11-18x)/(1-3x+x^2). [Philippe Deléham, Nov 16 2008]

a(n) = (11/2)*[(3/2)+(1/2)*sqrt(5)]^n-(3/10)*[(3/2)+(1/2)*sqrt4(5)]^n*sqrt(5)+(3/10)*[(3/2)-(1/2) *sqrt(5]^n*sqrt(5)+(11/2)*[(3/2)-(1/2)*sqrt(5)]^n, with n>=0. [Paolo P. Lava, Nov 19 2008]

a(n) = 4*Fibonacci(2n+1) + 7*Fibonacci(2n-1) = 4*Lucas(2n) + 3*Fibonacci(2n-1). [Ron Knott, Jul 01 2013]

MATHEMATICA

Table[6LucasL[2n]-Fibonacci[2n+2], {n, 0, 30}] (* or *) LinearRecurrence[ {3, -1}, {11, 15}, 30] (* Harvey P. Dale, Oct 02 2011 *)

PROG

(MAGMA) [8*Lucas(2*n) - Lucas(2*n+2) - 2*Fibonacci(2*n-1): n in [0..30]]; // Vincenzo Librandi, Oct 03 2011

CROSSREFS

Cf. A005248, A005248, A022133.

Sequence in context: A275242 A030099 A085597 * A032490 A068483 A241679

Adjacent sequences:  A097509 A097510 A097511 * A097513 A097514 A097515

KEYWORD

nonn,easy

AUTHOR

Creighton Dement, Aug 26 2004

EXTENSIONS

New definition from Ralf Stephan, Dec 01 2004

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 19 08:51 EST 2017. Contains 294923 sequences.