A014729 Squares of even Fibonacci numbers.

0, 4, 64, 1156, 20736, 372100, 6677056, 119814916, 2149991424, 38580030724, 692290561600, 12422650078084, 222915410843904, 4000054745112196, 71778070001175616, 1288005205276048900, 23112315624967704576, 414733676044142633476, 7442093853169599697984

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..700

Index entries for linear recurrences with constant coefficients, signature (17,17,-1)

Formula

a(n) = (1/5)*(Fibonacci(6*n+3) - 2*Fibonacci(6*n) - 2*(-1)^n). - Ralf Stephan, May 14 2004

G.f.: 4*(-x^2+x)/((1+x)*(1-18*x+x^2)). - Ralf Stephan, May 14 2004

a(n) = Fibonacci(3*n)^2. - Gary Detlefs, Nov 28 2010

a(n) = (-1)^(n+1)*(Fibonacci(n)*Fibonacci(7*n)-Fibonacci(4*n)^2). - Gary Detlefs, Nov 28 2010

a(n) = (-2*(-1)^n+(9+4*sqrt(5))^(-n)+(9+4*sqrt(5))^n)/5. - Colin Barker, Mar 04 2016

a(n) = A014445(n)^2. - Sean A. Irvine, Nov 18 2018

Mathematica

(Table[Fibonacci@ n, {n, 0, 55}] /. n_ /; OddQ@ n -> Nothing)^2 (* or *)
CoefficientList[Series[4 (-x^2 + x)/((1 + x) (1 - 18 x + x^2)), {x, 0, 18}], x] (* Michael De Vlieger, Mar 04 2016 *)

Prog

(MuPAD) numlib::fibonacci(3*n)^2 $ n = 0..25; // Zerinvary Lajos, May 09 2008
(Sage) [fibonacci(3*n)^2 for n in range(0, 17)] # Zerinvary Lajos, May 15 2009
(PARI) concat(0, Vec(4*x*(1-x)/((1+x)*(1-18*x+x^2)) + O(x^40))) \\ Colin Barker, Mar 04 2016
(Magma) [Fibonacci(3*n)^2: n in [0..20]]; // Vincenzo Librandi, Nov 19 2018

Crossrefs

Cf. A014445.

Sequence in context: A139292 A152923 A085807 * A322519 A259272 A361963

Adjacent sequences: A014726 A014727 A014728 * A014730 A014731 A014732

Keyword

nonn,easy

Author

Mohammad K. Azarian

Extensions

More terms from James A. Sellers

Status

approved