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A202299
y-values in the solution to x^2 - 18*y^2 = 1.
4
0, 4, 136, 4620, 156944, 5331476, 181113240, 6152518684, 209004522016, 7100001229860, 241191037293224, 8193395266739756, 278334248031858480, 9455171037816448564, 321197481037727392696, 10911259184244914903100
OFFSET
1,2
COMMENTS
The corresponding values of x of this Pell equation are in A056771.
LINKS
Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
FORMULA
a(n) = 34*a(n-1)-a(n-2) with a(1)=0, a(2)=4.
G.f.: 4*x^2/(1-34*x+x^2).
a(n) = (1/3)*A001542(2n-2). - Bruno Berselli, Dec 19 2011
MATHEMATICA
LinearRecurrence[{34, -1}, {0, 4}, 30]
PROG
(Magma) I:=[0, 4]; [n le 2 select I[n] else 34*Self(n-1)-Self(n-2): n in [1..20]];
(Maxima) makelist(expand(((3+2*sqrt(2))^(2*n-2)-(3-2*sqrt(2))^(2*n-2))/(6*sqrt(2))), n, 1, 16); /* _Bruno Berselli, Dec 19 2011 */
CROSSREFS
Sequence in context: A102986 A012160 A012197 * A024264 A012052 A054052
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Dec 18 2011
STATUS
approved