A154021 a(n+2) = 16*a(n+1) - a(n), with a(1)=0, a(2)=4.

0, 4, 64, 1020, 16256, 259076, 4128960, 65804284, 1048739584, 16714029060, 266375725376, 4245297576956, 67658385505920, 1078288870517764, 17184963542778304, 273881127813935100, 4364913081480183296

Offset

1,2

Comments

If a(n)=x and a(n+1)=y, then 16=(x^2+y^2)/(xy+1).

In general, the sequence a(1)=0, a(2)=U; a(n+2)=U^2*a(n+1)-a(n) has the property that "If a(n)=x and a(n+1)=y then (x^2+y^2)/(xy+1)=U^2".

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..800

Index entries for linear recurrences with constant coefficients, signature (16,-1).

Formula

From R. J. Mathar, Jan 05 2011: (Start)

G.f.: 4*x^2/(1 -16*x +x^2).

a(n) = 4*A077412(n-2). (End)

Mathematica

Nest[Append[#, 16Last[#]-#[[-2]]]&, {0, 4}, 20]  (* or *) Rest[CoefficientList[Series[4x^2/(1-16x+x^2), {x, 0, 22}], x]]  (* Harvey P. Dale, Apr 17 2011 *)
LinearRecurrence[{16, -1}, {0, 4}, 20] (* T. D. Noe, Apr 17 2011 *)

Prog

(Magma) I:=[0, 4]; [n le 2 select I[n] else 16*Self(n-1)-Self(n-2): n in [1..30]]; // Vincenzo Librandi, Feb 25 2012

Crossrefs

Cf. A065100, A154022-A154027.

Sequence in context: A268165 A026301 A010042 * A013709 A139292 A152923

Adjacent sequences: A154018 A154019 A154020 * A154022 A154023 A154024

Keyword

nonn,easy

Author

Vincenzo Librandi, Jan 04 2009

Extensions

375725376 replaced by 266375725376 - R. J. Mathar, Jan 07 2009

Edited by N. J. A. Sloane, Jun 23 2010 at the suggestion of Joerg Arndt.

Status

approved