A218735 Values of x in the solutions to x^2 - 3xy + y^2 + 29 = 0, where 0 < x < y.

5, 6, 9, 13, 22, 33, 57, 86, 149, 225, 390, 589, 1021, 1542, 2673, 4037, 6998, 10569, 18321, 27670, 47965, 72441, 125574, 189653, 328757, 496518, 860697, 1299901, 2253334, 3403185, 5899305, 8909654, 15444581, 23325777, 40434438, 61067677, 105858733

Offset: 1

Author

Colin Barker, Feb 05 2014

Keywords

• nonn
• easy

Comments

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

Positive values of x (or y) satisfying x^2 - 18xy + y^2 + 1856 = 0.

Examples

			13 is in the sequence because (x, y) = (13, 33) is a solution to x^2 - 3xy + y^2 + 29 = 0.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-1).

Crossrefs

Cf. A001519, A005248, A055819, A237132, A237133.

Programs

Mathematica

LinearRecurrence[{0,3,0,-1},{5,6,9,13},40] (* Harvey P. Dale, Nov 30 2024 *)

PARI

Vec(-x*(x-1)*(5*x^2+11*x+5)/((x^2-x-1)*(x^2+x-1)) + O(x^100))

Formula

a(n) = 3*a(n-2)-a(n-4).

G.f.: -x*(x-1)*(5*x^2+11*x+5) / ((x^2-x-1)*(x^2+x-1)).