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A162959 The pairs (x,y) such that (x^2 + y^2)/(x*y + 1) is a perfect square, i.e., 4. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 5 09:25 EST 2023. Contains 360084 sequences. (Running on oeis4.)