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A237254 Values of x in the solutions to x^2 - 5xy + y^2 + 5 = 0, where 0 < x < y. 4
1, 2, 3, 9, 14, 43, 67, 206, 321, 987, 1538, 4729, 7369, 22658, 35307, 108561, 169166, 520147, 810523, 2492174, 3883449, 11940723, 18606722, 57211441, 89150161, 274116482, 427144083, 1313370969, 2046570254, 6292738363, 9805707187, 30150320846, 46981965681 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The corresponding values of y are given by a(n+2).

Also the solutions to 21x^2-20 is a perfect square. - Jaimal Ichharam, Jul 13 2014

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,5,0,-1).

FORMULA

a(n) = 5*a(n-2)-a(n-4).

G.f.: -x*(x-1)*(x^2+3*x+1) / (x^4-5*x^2+1).

EXAMPLE

9 is in the sequence because (x, y) = (9, 43) is a solution to x^2 - 5xy + y^2 + 5 = 0.

MAPLE

A237254 := proc(n)

    coeftayl( -x*(x-1)*(x^2+3*x+1) / (x^4-5*x^2+1), x=0, n);

end proc:

seq(A237254(n), n=1..40); # Wesley Ivan Hurt, Jul 14 2014

MATHEMATICA

Rest[CoefficientList[Series[- x (x - 1) (x^2 + 3 x + 1)/(x^4 - 5 x^2 + 1), {x, 0, 40}], x]] (* Vincenzo Librandi, Jul 01 2014 *)

PROG

(PARI) Vec(-x*(x-1)*(x^2+3*x+1)/(x^4-5*x^2+1) + O(x^100))

CROSSREFS

Cf. A004253, A237255.

Sequence in context: A094557 A222658 A227212 * A026307 A139816 A083303

Adjacent sequences:  A237251 A237252 A237253 * A237255 A237256 A237257

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Feb 05 2014

STATUS

approved

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Last modified September 22 20:30 EDT 2018. Contains 315270 sequences. (Running on oeis4.)