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A281504 Solutions y to the negative Pell equation y^2 = 33*x^2 - 8 with x,y >= 0. 2
5, 17, 247, 787, 11357, 36185, 522175, 1663723, 24008693, 76495073, 1103877703, 3517109635, 50754365645, 161710548137, 2333596941967, 7435168104667, 107294704964837, 341856022266545, 4933222831440535, 15717941856156403, 226820955541299773, 722683469360927993 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
M. A. Gopalan, S. Vidhyalakshmi, E. Premalatha, R. Janani, On The Negative Pell Equation y^2 = 33*x^2 - 8, International Journal of Multidisciplinary Research and Modern Education (IJMRME), Volume II, Issue I, 2016.
FORMULA
a(n) = 46*a(n-2) - a(n-4) for n>4.
G.f.: x*(1 + x)*(5 + 12*x + 5*x^2) / (1 - 46*x^2 + x^4).
EXAMPLE
17 is in the sequence because (x, y) = (3, 17) is a solution to y^2 = 33*x^2 - 8.
MATHEMATICA
LinearRecurrence[{0, 46, 0, -1}, {5, 17, 247, 787}, 30] (* Harvey P. Dale, Sep 06 2023 *)
PROG
(PARI) Vec(x*(1 + x)*(5 + 12*x + 5*x^2) / (1 - 46*x^2 + x^4) + O(x^30))
CROSSREFS
Cf. A281503.
Sequence in context: A103920 A086362 A195570 * A191500 A089894 A077718
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 23 2017
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)