A162959 The pairs (x,y) such that (x^2 + y^2)/(x*y + 1) is a perfect square, i.e., 4.

0, 2, 2, 8, 8, 30, 30, 112, 112, 418, 418, 1560, 1560, 5822, 5822, 21728, 21728, 81090, 81090, 302632, 302632, 1129438, 1129438, 4215120, 4215120, 15731042, 15731042, 58709048, 58709048, 219105150, 219105150, 817711552, 817711552, 3051741058, 3051741058, 11389252680, 11389252680

Offset

1,2

Comments

Essentially A052530, each term besides the first repeated. - R. J. Mathar, Jul 21 2009

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,4,0,-1).

Formula

From Colin Barker, Feb 21 2013: (Start)

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

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

Example

Pairs are (8,30) with (8^2 + 30^2)/(8*30 + 1) = 4, or (30,112) with (30^2 + 112^2)/(30*112 + 1) = 4.

Mathematica

CoefficientList[Series[2 x (x + 1) / (x^4 - 4 x^2 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, May 14 2013 *)

Prog

(PARI) x='x+O('x^66); concat([0], Vec(2*x^2*(x+1)/(x^4-4*x^2+1))) \\ Joerg Arndt, May 15 2013

Crossrefs

Sequence in context: A073090 A120544 A155950 * A354830 A158302 A007083

Adjacent sequences: A162956 A162957 A162958 * A162960 A162961 A162962

Keyword

nonn,less,easy

Author

Vincenzo Librandi, Jul 19 2009

Status

approved