A237254 Values of x in the solutions to x^2 - 5xy + y^2 + 5 = 0, where 0 < x < y.

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

Offset: 1

Author

Colin Barker, Feb 05 2014

Keywords

• nonn
• easy

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

Examples

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

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).

Crossrefs

Cf. A004253, A237255.

Programs

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 *)
LinearRecurrence[{0,5,0,-1},{1,2,3,9},40] (* Harvey P. Dale, Aug 24 2024 *)

PARI

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

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).