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

Author

Mohammad K. Azarian

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..700
• Index entries for linear recurrences with constant coefficients, signature (17,17,-1)

Crossrefs

Cf. A014445.

Programs

Magma

[Fibonacci(3*n)^2: n in [0..20]]; // Vincenzo Librandi, Nov 19 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 *)
LinearRecurrence[{17,17,-1},{0,4,64},20] (* Harvey P. Dale, Aug 02 2024 *)

MuPAD

numlib::fibonacci(3*n)^2 $ n = 0..25; // Zerinvary Lajos, May 09 2008

PARI

concat(0, Vec(4*x*(1-x)/((1+x)*(1-18*x+x^2)) + O(x^40))) \\ Colin Barker, Mar 04 2016

Sage

[fibonacci(3*n)^2 for n in range(0, 17)] # Zerinvary Lajos, May 15 2009

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

Extensions

More terms from James Sellers