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A237132 Values of x in the solutions to x^2 - 3xy + y^2 + 11 = 0, where 0 < x < y. 4
3, 4, 5, 9, 12, 23, 31, 60, 81, 157, 212, 411, 555, 1076, 1453, 2817, 3804, 7375, 9959, 19308, 26073, 50549, 68260, 132339, 178707, 346468, 467861, 907065, 1224876, 2374727, 3206767, 6217116, 8395425, 16276621, 21979508, 42612747, 57543099, 111561620 (list; graph; refs; listen; history; text; internal format)
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 + 704 = 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).

FORMULA

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

G.f.: -x*(x-1)*(3*x^2+7*x+3) / ((x^2-x-1)*(x^2+x-1)).

a(n) = F(n+2) + (-1)^n*F(n-3), n>1, with F the Fibonacci numbers (A000045). - Ralf Stephan, Feb 05 2014

EXAMPLE

9 is in the sequence because (x, y) = (9, 23) is a solution to x^2 - 3xy + y^2 + 11 = 0.

PROG

(PARI) Vec(-x*(x-1)*(3*x^2+7*x+3)/((x^2-x-1)*(x^2+x-1)) + O(x^100))

CROSSREFS

Cf. A001519, A005248, A055819, A237133, A218735.

Sequence in context: A166976 A240056 A235396 * A080633 A026488 A242800

Adjacent sequences:  A237129 A237130 A237131 * A237133 A237134 A237135

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Feb 04 2014

STATUS

approved

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Last modified October 20 11:11 EDT 2018. Contains 316379 sequences. (Running on oeis4.)