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A081074 Fibonacci(4n)-3, or Fibonacci(2n-2)*Lucas(2n+2). 0
0, 18, 141, 984, 6762, 46365, 317808, 2178306, 14930349, 102334152, 701408730, 4807526973, 32951280096, 225851433714, 1548008755917, 10610209857720, 72723460248138, 498454011879261, 3416454622906704, 23416728348467682 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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..20.

Index entries for linear recurrences with constant coefficients, signature (8,-8,1).

FORMULA

a(n) = 8a(n-1) - 8a(n-2) + a(n-3).

a(n) = -3+(3/2)*{[(7/2)-(3/2)*sqrt(5)]^n+[(7/2)+(3/2)*sqrt(5)]^n}+(7/10)*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.: 3*x^2*(-6+x) / ( (x-1)*(x^2-7*x+1) ). a(n) = A033888(n)-3. - R. J. Mathar, Sep 03 2010

MAPLE

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

PROG

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

CROSSREFS

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

Sequence in context: A212154 A108680 A204273 * A299062 A299723 A125355

Adjacent sequences:  A081071 A081072 A081073 * A081075 A081076 A081077

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 January 19 09:35 EST 2020. Contains 331048 sequences. (Running on oeis4.)