A014731 Squares of even Lucas numbers.

4, 16, 324, 5776, 103684, 1860496, 33385284, 599074576, 10749957124, 192900153616, 3461452808004, 62113250390416, 1114577054219524, 20000273725560976, 358890350005878084, 6440026026380244496, 115561578124838522884, 2073668380220713167376

Offset

0,1

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

G.f.: 4*(-4*x^2-13*x+1)/((1+x)*(1-18*x+x^2)). - Ralf Stephan, May 14 2004

From Colin Barker, Mar 04 2016: (Start)

a(n) = 2*(-1)^n+(9+4*sqrt(5))^(-n)+(9+4*sqrt(5))^n.

a(n) = 17*a(n-1)+17*a(n-2)-a(n-3) for n>2. (End)

a(n) = A014448(n)^2. - Sean A. Irvine, Nov 18 2018

a(n) = 5*Fibonacci(3*n)^2 + 4*(-1)^n. - Amiram Eldar, Jan 11 2022

Mathematica

(Table[LucasL@ n, {n, 0, 52}] /. n_ /; OddQ@ n -> Nothing)^2 (* Michael De Vlieger, Mar 04 2016 *)
LinearRecurrence[{17, 17, -1}, {4, 16, 324}, 20] (* Harvey P. Dale, Nov 19 2024 *)

Prog

(PARI) Vec(4*(1-13*x-4*x^2)/((1+x)*(1-18*x+x^2)) + O(x^20)) \\ Colin Barker, Mar 04 2016

Crossrefs

Cf. A000045, A014448.

Sequence in context: A203105 A273474 A095956 * A023114 A207851 A202681

Adjacent sequences: A014728 A014729 A014730 * A014732 A014733 A014734

Keyword

nonn,easy

Author

Mohammad K. Azarian

Extensions

More terms from Erich Friedman.

Status

approved