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A081004 Fibonacci(4n+2)+1, or Fibonacci(2n+2)*Lucas(2n). 1
2, 9, 56, 378, 2585, 17712, 121394, 832041, 5702888, 39088170, 267914297, 1836311904, 12586269026, 86267571273, 591286729880, 4052739537882, 27777890035289, 190392490709136, 1304969544928658, 8944394323791465, 61305790721611592, 420196140727489674 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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..600

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.: (7*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+2)+1) od: # James A. Sellers, Mar 03 2003

MATHEMATICA

Table[Fibonacci[4 n + 2] + 1, {n, 0, 20}] (* Wesley Ivan Hurt, Nov 20 2014 *)

PROG

(MAGMA) [Fibonacci(4*n+2)+1: n in [0..100]]; // Vincenzo Librandi, Apr 15 2011

CROSSREFS

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

Sequence in context: A240562 A091108 A179405 * A198953 A212392 A186262

Adjacent sequences:  A081001 A081002 A081003 * A081005 A081006 A081007

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 May 26 05:25 EDT 2019. Contains 323579 sequences. (Running on oeis4.)