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A237262 Values of x in the solutions to x^2 - 8*x*y + y^2 + 11 = 0, where 0 < x < y. 6
1, 2, 6, 15, 47, 118, 370, 929, 2913, 7314, 22934, 57583, 180559, 453350, 1421538, 3569217, 11191745, 28100386, 88112422, 221233871, 693707631, 1741770582, 5461548626, 13712930785, 42998681377, 107961675698, 338527902390, 849980474799, 2665224537743 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The corresponding values of y are given by a(n+2).
Also values of y in the solutions to the negative Pell equation x^2 - 15*y^2 = -11. - Colin Barker, Jan 25 2017
LINKS
FORMULA
G.f.: -x*(x-1)*(x^2 + 3*x + 1) / (x^4 - 8*x^2 + 1).
a(n) = 8*a(n-2) - a(n-4) for n > 4.
a(n) = (11*a(n-1) - 4*a(n-2))/3 if n is odd; a(n) = (11*a(n-1) - 3*a(n-2))/4 if n is even. - R. J. Mathar, Jun 18 2014
EXAMPLE
6 is a term because (x, y) = (6, 47) is a solution to x^2 - 8xy + y^2 + 11 = 0.
MATHEMATICA
LinearRecurrence[{0, 8, 0, -1}, {1, 2, 6, 15}, 30] (* Harvey P. Dale, Sep 06 2020 *)
PROG
(PARI) Vec(-x*(x-1)*(x^2+3*x+1)/(x^4-8*x^2+1) + O(x^100))
CROSSREFS
For first and second differences see A322780, A199336.
Sequence in context: A045628 A186738 A127383 * A291848 A363207 A196961
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Feb 05 2014
STATUS
approved

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)