

A081010


a(n) = Fibonacci(4n+1) + 2, or Fibonacci(2n1)*Lucas(2n+2).


1



3, 7, 36, 235, 1599, 10948, 75027, 514231, 3524580, 24157819, 165580143, 1134903172, 7778742051, 53316291175, 365435296164, 2504730781963, 17167680177567, 117669030460996, 806515533049395, 5527939700884759, 37889062373143908, 259695496911122587
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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..500
Index entries for linear recurrences with constant coefficients, signature (8,8,1).


FORMULA

a(n) = 8*a(n1)  8*a(n2) + a(n3).
a(n) = 2 + (A001906(n+1)^2 + A001519(n)^2)/2.  Creighton Dement, Aug 15 2004
a(n) = 2+(1/2)*{[(7/2)(3/2)*sqrt(5)]^n+[(7/2)+(3/2)*sqrt(5)]^n}+(1/10)*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.: (317*x+4*x^2)/((1x)*(17*x+x^2)).  Colin Barker, Jun 24 2012


MAPLE

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


MATHEMATICA

Fibonacci[4*Range[0, 30]+1]+2 (* G. C. Greubel, Jul 14 2019 *)


PROG

(MAGMA) [Fibonacci(4*n+1) +2: n in [0..30]]; // Vincenzo Librandi, Apr 15 2011
(PARI) vector(30, n, n; fibonacci(4*n+1)+2) \\ G. C. Greubel, Jul 14 2019
(Sage) [fibonacci(4*n+1)+2 for n in (0..30)] # G. C. Greubel, Jul 14 2019
(GAP) List([0..30], n> Fibonacci(4*n+1)+2); # G. C. Greubel, Jul 14 2019


CROSSREFS

Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers).
Sequence in context: A102917 A156465 A049366 * A100377 A270396 A167169
Adjacent sequences: A081007 A081008 A081009 * A081011 A081012 A081013


KEYWORD

nonn,easy


AUTHOR

R. K. Guy, Mar 01 2003


EXTENSIONS

More terms from James A. Sellers, Mar 03 2003


STATUS

approved



