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A081008 a(n) = Fibonacci(4n+2) - 1, or Fibonacci(2n)*Lucas(2n+2). 1
0, 7, 54, 376, 2583, 17710, 121392, 832039, 5702886, 39088168, 267914295, 1836311902, 12586269024, 86267571271, 591286729878, 4052739537880, 27777890035287, 190392490709134, 1304969544928656, 8944394323791463, 61305790721611590, 420196140727489672 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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 = 0..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+(1/2)*{[(7/2)-(3/2)*sqrt(5)]^n+[(7/2)+(3/2)*sqrt(5)]^n}+(3/10)*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*(7-2*x)/((1-x)*(1-7*x+x^2)). - Colin Barker, Jun 24 2012

MAPLE

with(combinat) for n from 0 to 30 do printf(`%d, `, fibonacci(4*n+2)-1) od # James A. Sellers, Mar 03 2003

PROG

(MAGMA) [Fibonacci(4*n+2)-1: n in [0..30]]; // Vincenzo Librandi, Apr 15 2011

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

(Sage) [fibonacci(4*n+2)-1 for n in (0..30)] # G. C. Greubel, Jul 14 2019

(GAP) List([0..30], n-> Fibonacci(4*n+2)-1); # G. C. Greubel, Jul 14 2019

CROSSREFS

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

Sequence in context: A116202 A203289 A204258 * A116472 A015562 A243670

Adjacent sequences:  A081005 A081006 A081007 * A081009 A081010 A081011

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 December 10 20:38 EST 2019. Contains 329909 sequences. (Running on oeis4.)