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

Author

Vincenzo Librandi, Jul 19 2009

Keywords

• nonn
• less
• easy

Comments

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

Examples

			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.
		

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).

Programs

Mathematica

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

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

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)