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A218735
Values of x in the solutions to x^2 - 3xy + y^2 + 29 = 0, where 0 < x < y.
3
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
1,1
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.
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)).
EXAMPLE
13 is in the sequence because (x, y) = (13, 33) is a solution to x^2 - 3xy + y^2 + 29 = 0.
MATHEMATICA
LinearRecurrence[{0, 3, 0, -1}, {5, 6, 9, 13}, 40] (* Harvey P. Dale, Nov 30 2024 *)
PROG
(PARI) Vec(-x*(x-1)*(5*x^2+11*x+5)/((x^2-x-1)*(x^2+x-1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Feb 05 2014
STATUS
approved