|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|